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Optimum Control of Parabolic Trough Solar Fields with Partial Radiation*
Proceedings of the 20th World Congress Proceedings of 20th Proceedings of the the 20th World World Congress The International Federation of Congress Automatic Control Proceedings of the 20th World The International Federation of Automatic Control The International Federation of Congress Automatic Control Toulouse, France, July 9-14, 2017 Available online at www.sciencedirect.com The International of Automatic Control Toulouse, France, July Toulouse, France,Federation July 9-14, 9-14, 2017 2017 Toulouse, France, July 9-14, 2017
ScienceDirect
IFAC PapersOnLine 50-1 (2017) 109–114
Optimum Optimum Control Control Optimum Control Solar Fields Solar Fields with with Solar Fields with ∗
of of Parabolic Parabolic Trough Trough ⋆ of Parabolic Trough Partial Radiation Partial Radiation ⋆⋆ Partial ∗∗Radiation ∗∗∗
Sergio J. Navas ∗ Francisco R. Rubio ∗∗ Pedro Ollero ∗∗∗ Sergio Sergio J. J. Navas Navas ∗ Francisco Francisco R. R. Rubio Rubio ∗∗ Pedro Pedro Ollero Ollero ∗∗∗ Sergio J. Navas ∗ Francisco R. Rubio ∗∗ Pedro Ollero ∗∗∗ ∗ ıa de Sistemas y Autom´ atica, Universidad ∗ Departamento de Ingenier´ ∗ Departamento de Ingenier´ ıa Sistemas a de Ingenier´ ıa de de(e-mail:[email protected]). Sistemas yy Autom´ Autom´ atica, tica, Universidad Universidad de Sevilla, Spain ∗ Departamento de Ingenier´ ıa de(e-mail:[email protected]). Sistemas y Autom´ atica, Universidad de Sevilla, Spain ∗∗Departamento de Sevilla, Spain (e-mail:[email protected]). Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ de de Sevilla, Spain (e-mail:[email protected]). ∗∗ Departamento Ingenier´ ıa Sistemas yy Autom´ a Ingenier´ ıa de de(e-mail: Sistemas Autom´ atica, tica, Universidad Universidad Spain [email protected]) ∗∗ DepartamentodedeSevilla, deSevilla, Ingenier´ ıa de(e-mail: Sistemas y Autom´ atica, Universidad Spain [email protected]) ∗∗∗Departamentode de Sevilla, Spain (e-mail: [email protected]) Departamento de Ingenier´ ıa Qu´ ımica y Ambiental, Universidad de ∗∗∗ de de Sevilla, Spain (e-mail: [email protected]) ∗∗∗ Departamento ıa Qu´ de Ingenier´ Ingenier´ ıa(e-mail: Qu´ımica ı[email protected]) y Ambiental, Ambiental, Universidad Universidad de de Spain ∗∗∗ DepartamentoSevilla, DepartamentoSevilla, de Ingenier´ Qu´ı[email protected]) y Ambiental, Universidad de Spainıa(e-mail: (e-mail: Sevilla, Spain [email protected]) Sevilla, Spain (e-mail: [email protected]) Abstract: This paper describes the main problems of operating parabolic trough solar fields Abstract: describes the main problems of trough solar Abstract: This paper describes the An mainoptimal problems of operating operating parabolic trough solar fields fields during daysThis withpaper partial radiation. control strategyparabolic is proposed to solve these Abstract: This paper describes the An main problems of operating parabolic trough solar fields during with partial control strategy is to these during days days with partial radiation. radiation. An optimal optimal control strategy is proposed proposed toPIsolve solve these problems and it is assessed against a classical one, which uses a feedforward and a controller during days with partial radiation. An optimal control strategy is proposed to solve these problems and it is assessed against a classical one, which uses a feedforward and a PI controller problems and set it is point assessed against a classical one, which uses a feedforward and a PI controller with a fixed of oil outlet temperature. Some simulations have been made using problems and it is assessed against a classical one, which uses a feedforward and a PI controller with set outlet Some simulations made using with aa fixed fixed set point point of of oil oil using outlet temperature. temperature. Some simulations have been made using MATLAB to demonstrate optimal control strategy better have resultsbeen can be achieved. with a fixed set point ofthat oil outletthe temperature. Some simulations have been made using MATLAB MATLAB to to demonstrate demonstrate that that using using the the optimal optimal control control strategy strategy better better results results can can be be achieved. achieved. MATLAB to (International demonstrate Federation that usingofthe optimalControl) control Hosting strategy results can be achieved. © 2017, IFAC Automatic bybetter Elsevier Ltd. All rights reserved. Keywords: Solar, Control, Optimization, Parabolic Trough, Simulation, Partial Radiation Keywords: Solar, Solar, Control, Control, Optimization, Optimization, Parabolic Parabolic Trough, Trough, Simulation, Simulation, Partial Partial Radiation Radiation Keywords: Keywords: Solar, Control, Optimization, Parabolic Trough, Simulation, Partial Radiation 1. INTRODUCTION On the other hand, using a PI with a feedforward controller 1. INTRODUCTION INTRODUCTION On other PI aa feedforward controller 1. On the the other hand, hand, using using PI with with feedforward controller that manipulates oil aaaflow to keep constant the outlet 1. INTRODUCTION On the other hand,the using PI with a feedforward controller that manipulates the oil flow to keep constant the outlet that manipulates the oil flow to keep constant the outlet of the field, like in Camacho et al. (1997)The main technologies for converting solar energy into temperature that manipulates thefield, oil flow to keep constant the(1997)outlet temperature of the like in Camacho et al. The main technologies for converting solar energy into temperature of the field, like in Camacho et al. (1997)et al. (2012)-Carmona (1985), while a cloud is The main are technologies for (PV) converting solar energy solar into Camacho electricity photovoltaic and concentrated temperature of the field, like in Camacho et al. (1997)The main technologies for converting solar energy into Camacho et al. (2012)-Carmona (1985), while a cloud is electricity(CST). are photovoltaic photovoltaic (PV) and and concentrated solar passing Camacho et al. (2012)-Carmona (1985), while a cloud is through the field may provoke temperature peaks electricity are (PV) concentrated solar thermal Parabolic trough, solar towers, Fresnel Camacho et al. (2012)-Carmona (1985), while a cloud is electricity are photovoltaic (PV) and concentrated solar passing through the field may provoke temperature peaks thermal (CST). Parabolic trough, solar towers, Fresnel passing through the field may provoke temperature peaks in some loops. This situation is due to the fact that when thermal (CST). Parabolic trough, solar towers, Fresnel collector and solar dishes are the most used technolopassing through the field may provoke temperature peaks thermal (CST). Parabolic trough, towers, Fresnel in some due to when collector and solar solar dishes are the solar most used technolotechnolosome loops. This situation iswill duedecrease to the the fact fact that when the cloudloops. passesThis the situation controlleris the that oil flow in collector and dishes the most used gies for concentrating solar are energy. This paper focus on in in some loops. This situation iswill duedecrease to the fact that when collector and solar dishes are the most used technolothe cloud passes the controller the oil flow in gies for concentrating solar energy. This paper focus on the cloud passes the controller will decrease the oil flow in to keep the outlet temperature constant, however, gies for concentrating solar energy. This paper focus on order parabolic trough solar fields, which consist of a collector the cloud passes the controller will decrease the oil flow in gies for concentrating solar energy. This paper focus on order to keep the outlet temperature constant, however, parabolic trough solar fields, which consist of a collector order to keep the outlet temperature constant, however, in the loops that are not covered by the cloud, the solar parabolic trough solar fields, which consist of a collector field (Fig. trough 1), a power and auxiliary elements such as order to keepthat the are outlet temperature constant, however, parabolic solarcycle fields, which consist of a collector in the loops not covered by the cloud, the solar field (Fig. 1), a power cycle and auxiliary elements such as in the loops thatreduced, are not covered thetemperature cloud, the solar is not so that by their will field (Fig. 1), aand power cycleThe andsolar auxiliary elements such as radiation pumps, pipes valves. collector field collects the loops thatreduced, are not covered by the cloud, the solar field (Fig. 1), aand power cycleThe andsolar auxiliary elements such as in radiation is so their will pumps, pipes valves. collector field collects collects radiation is not not reduced, so that that limit. their temperature temperature will be increased above the security If this situation pumps, pipes and valves. The solaracollector field solar radiation and focuses it onto tube in which a heat radiation is not reduced, so that limit. their temperature will pumps, pipes and valves. The solaracollector field collects be increased above the security If this situation solar radiation and focuses it onto tube in which a heat be increased above the security limit. If this situation the collectors aresecurity programmed toIfget outsituation of focus solar radiation and focuses it onto tube in which heat transfer fluid, usually synthetic oil,aa circulates. Theaa oil is happens be increased above the limit. this solar radiation and focuses it onto tube in which heat happens the collectors are programmed to get out of focus transferup fluid, usually synthetic oil, circulates. The oil is is to happens the are programmed to involve get out aofloss focus prevent oilcollectors degradation, but that would of transfer fluid, synthetic circulates. oil heated andusually then used by theoil, power cycle toThe produce the collectors are programmed to involve get out aofloss focus transfer fluid, usually synthetic circulates. oil is happens to oil degradation, but would heated up up andmeans then of used by the theoil, power cycle to toThe produce to prevent prevent oil degradation, but that that would involve a loss of of energy and it is not considered in this paper as a possible heated and then used by power cycle produce electricity by a turbine. prevent but that would involve a loss of heated up by andmeans then of usedturbine. by the power cycle to produce to energy andoil it degradation, is not not considered considered in this this paper as aa possible possible electricity energy and it is in paper as solution. electricity by means of aa turbine. energy and it is not considered in this paper as a possible electricity by means of a turbine. solution. solution. The main goal of a parabolic trough solar field is to solution. The main main goal of aa parabolic parabolic trough solar to field is to to In this paper the effect of the solar radiation on the outlet The of trough solar field is collect the goal maximum solar energy in order produce The main goal of a parabolic trough solar to field is to In of solar the collect the maximum solar energy in order produce In this this paper paper the the effect of the the solar radiation on the outlet outlet was effect studied with a radiation complete on power cycle collect maximum solarasenergy in order to produce as muchthe electrical power possible. Normally, this is temperature In this paper the effect of the solar radiation on the outlet collect the maximum solar energy in order to produce temperature was studied with a complete power cycle as much electrical power as possible. Normally, this is temperature was studied with a complete power cycle model (Fig. 2) reduced to a correlation that relates the as much electrical power as possible. Normally, this is achieved keepingpower the outlet temperature of the field temperature was studiedto with a complete power cycle as much by electrical as possible. Normally, this is model (Fig. 2) reduced a correlation that relates the achieved by keeping the outlet temperature of the field model (Fig. 2) reduced to abycorrelation that relates the ◦ electrical power generated the condensation turbine achieved bymaximum keeping the outlet value, temperature of the field around the allowable that is 400 C, due model (Fig. 2) reduced to abycorrelation that relates the ◦ achieved bymaximum keeping the outlet value, temperature of the electrical power generated the condensation turbine ◦ C, field around the allowable that is 400 due electrical power generated by the condensation turbine the mass flow and outlet temperature of the oil. In around the maximum allowable value, that iswe400 due with to oil degradation. However, in this paper, will ◦ C,show electrical power generated by the condensation turbine around the maximum allowable value, that is 400 C, due with the mass flow and outlet temperature of the oil. to oil degradation. However, in this paper, we will with the mass flow and outletit temperature of the oil. In In Camacho and Gallego (2013) is used a similar approach to oilthis degradation. However, in thisdoes paper, we will show show that way to operate the field not produce the with the mass flow and outlet temperature of the oil. In to oilthis degradation. However, in thisdoes paper, we will show Camacho and Gallego (2013) it is used aa similar approach that way to operate the field not produce the Camacho and Gallego (2013) it is used similar approach but they use a correlation that only depends on the outlet that this way to operate the field does not produce the best results of electrical power generated. This problem Camacho and Gallego (2013) it is used a similar approach that results this wayof to operate power the field does notThis produce the but but they they use use aa correlation correlation that only only depends depends on the the outlet best generated. that on outlet implies efficiency higher than the best been results of electrical electrical power generated. problem has studied before in Lippke (1995), This whereproblem it was temperature, but they use athat correlation that onlyresults depends on the outlet best results of electrical power generated. This problem temperature, that implies efficiency results higher than the has been studied before in Lippke (1995), where it was temperature, that implies efficiency results higher than the found in the literature Lippke (1995); in addition has been studied before in strategy Lippke (1995), where it was ones suggested that the optimum is based on adapting that implies efficiency results higher than the has been studied before in strategy Lippke (1995), where it was temperature, ones found in the literature Lippke (1995); in addition the suggested that the optimum is based on adapting ones found in the literature Lippke (1995); in addition the simulations made in this paper were carried out taking suggested that the optimum strategy is based on adapting the fluid outlet temperature the incident solar found inmade the literature Lippke (1995); in addition the suggested that the optimumto strategy is based onradiation, adapting ones simulations in this paper were carried out taking the fluid outlet temperature to the incident solar radiation, simulations made in this paper were carried out taking into account a model of the entire field, not assuming the fluid outlet temperature to the incident solar radiation, keeping the constant the superheating temperature of the simulations made in this paper were carried out taking the fluid the outlet temperature to the incident solar radiation, account aa model the entire field, not assuming keeping constant the temperature of into account model of loop the is entire field, than not the assuming that the behavior of oneof the same other keepingitthe constant the superheating superheating temperature of the the into steam; was also studied in Montes et al. (2009) where account a model of loop the is entire field, than not the assuming keeping the constant the superheating temperature of the into that the behavior of one the same other steam; it was also studied in Montes et al. (2009) where that the behavior of one loop is the same than the other ◦ ones. Therefore, the authors propose that using an optimal it was alsotemperature studied in Montes et (393 al. (2009) where asteam; constant outlet was used C). Finally, that the behavior of one loop is the same than the other ◦ steam; it was also studied in Montes et al. (2009) where ones. Therefore, the authors propose that using an optimal ◦ aa constant outlet temperature was used (393 C). Finally, ones. Therefore, the authors propose that using an optimal controller with constraints can prevent the appearance of constant outlet temperature was used (393 C). Finally, more recent study was carried out in Camacho and ones. ◦ Therefore, the authorscan propose thatthe using an optimal a constant outlet temperature was used (393 C). Finally, controller with constraints prevent appearance of aaGallego more recent study was carried out in Camacho and controller with constraints can prevent the appearance of temperature peaks and also maximize the electrical power more (2013) recent where study itwas carried out in Camacho and was carried proposed to in change the outlet with constraints can preventthe theelectrical appearance of a more (2013) recent where study itwas out Camacho and controller temperature peaks and also maximize power Gallego was proposed to change the outlet temperature peaks and also maximize the electrical power generated by the field depending on the value of solar Gallego (2013) where itaccording was proposed to value changeofthe outlet temperature set point to the the solar temperature peaks and also maximize the electrical power Gallego (2013) where it was proposed to change the outlet generated by the field depending on the value of solar temperature the field depending on the value of solar radiation. by temperature set set point point according according to to the the value value of of the the solar solar generated radiation. by the field depending on the value of solar temperature set point according to the value of the solar generated radiation. radiation. radiation. radiation. radiation. radiation. The paper is organized as follows: Section 2 describes the ⋆ This work was supported by the projects DPI2013-44135-R and The is as follows: Section 22 describes the The paper paper is organized organized as passing follows: clouds Sectionand describes the ⋆ models of the solar field, power cycle This work was supported by the projects DPI2013-44135-R and ⋆ The paper is organized as passing follows: clouds Sectionand 2 describes the This work was supported by the projects DPI2013-44135-R and DPI2015-70973-R granted by the Spanish Ministry of Science models of the solar field, power cycle ⋆ models ofsimulation the solar field, passing cloudsIIIand power cycle This work was supported bythe theSpanish projectsMinistry DPI2013-44135-R used for purposes. Section describes both DPI2015-70973-R granted by of Science and DPI2015-70973-R granted by the Spanish Ministry of Science and models of the solar field, passing clouds and power cycle Innovation. used for for simulation simulation purposes. purposes. Section Section III III describes describes both both DPI2015-70973-R granted by the Spanish Ministry of Science and used Innovation. Innovation. used for simulation purposes. Section III describes both Innovation.
Copyright © 2017, 2017 IFAC 111 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2017 IFAC 111 Copyright ©under 2017 responsibility IFAC 111Control. Peer review of International Federation of Automatic Copyright © 2017 IFAC 111 10.1016/j.ifacol.2017.08.019
Proceedings of the 20th IFAC World Congress 110 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
control strategies tested: the feedforward with a PI control and the optimum control. Section IV shows the results obtained by simulations made in MATLAB. Finally, the paper draws to a close with some concluding remarks.
differential equations describing the energy balance: Active zones
ρm Cm Am
∂Tm = In0 G − Hl G(Tm − Ta ) − ∂t LHt (Tm − Tf )
(1)
Fluid element ρf Cf Af
∂Tf ∂Tf + ρf Cf q˙ = LHt (Tm − Tf ) ∂t ∂x
(2)
Passive zones Fig. 1. ACUREX distributed solar collector field ρm Cm Am
∂Tm = −Hp (Tm − Ta ) − LHt (Tm − Tf ) ∂t
(3)
where the sub-index m refers to metal and f refers to the fluid. The model parameters and their units are shown in table 1. Table 1. Solar field model parameters description
Fig. 2. Diagram of the solar field connected with the power cycle
Symbol t x ρ C A T q˙ I n0 G Ta Hl
2. SYSTEM MODELING
Ht
The model of each of the parts which have been used to simulate the operation of a solar field during the days with partial covering is presented. These parts are: the solar collector field, the passage of the clouds and the power cycle.
Hp
2.1 Solar Collector Field Model In this subsection, the mathematical model of a parabolic trough solar field is presented. This model is the same used in Navas et al. (2016) which is at the same time a slight modification of the model proposed by Camacho et al. (1997)-Camacho et al. (2012)-Carmona (1985) for the ACUREX field (Fig. 1). Basically, this model can be used to simulate parabolic trough solar fields by selecting parameters like the number of active (the parts where the solar radiation reaches the tube) and passive (joints and other parts not reached by concentrated solar radiation) zones, length of each zone, or collector aperture. The solar field simulated in this paper is supposed to be on the site of the Escuela Superior de Ingenier´ıa de Sevilla. It is composed of 24 loops and has dimensions of 144x240 m2 . Each loop is modeled by the following system of partial 112
L
Description Time Space Density Specific heat capacity Cross sectional area Temperature Oil flow rate Solar radiation Optical efficiency Collector aperture Ambient Temperature Global coefficient of thermal losses for active zones Coefficient of heat transmission metal-fluid Global coefficient of thermal losses for passive zones Length of pipe line
Units s m Kg/m3 J/(K kg) m2 ◦C m3 /s W/m2 Unit-less M ◦C W/(m2 ◦ C) W/(m2 ◦ C) W/(m2 ◦ C) m
The density ρ, specific heat C and coefficient of thermal loss Hl depend on fluid temperature. The coefficient of heat transmission Ht depends on temperature and oil flow. The incident solar radiation I depends on hourly angle, solar hour, declination, Julianne day, local latitude and collector dimensions Camacho et al. (1997)-Camacho et al. (2012)-Carmona (1985). In order to solve this system of partial differential equations, a two stage finite difference equation has been programmed, considering each segment of 1 m for the passive zones and of 3 m for the active zones and solving (1)-(2)-(3). 2.2 Modeling of the Passing Clouds The modeling of the passing clouds is necessary to know how the radiation of the sun is distributed throughout the field. This can be achieved creating a matrix which represents the whole field extension. Each element of the matrix is assigned the value of the incident solar radiation
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114
on that section at each time. The solar field has dimensions of 144x240 m2 , so if we divide the matrix in elements of 3x3 meters we need a 48x80 matrix. The matrix is then put over the field in such a way that each element contains a fraction of an active or passive element. Fig.3 shows the fraction of the whole matrix that covers one loop of a generic field.
111
returning to the field respectively. This simplification was necessary to reduce the simulation time and the error is around 1%. In addition the dynamic of the cycle was assumed to be like a first order model with a time constant of 100 seconds. W = 8.23e3 − 49.96moil − 2.70m2oil −
2 + 5.38e−1 moil Tout 47.15Tout + 6.75e−2 Tout
Tin = 3.40e2 + 1.78moil − 1.55e−1 m2oil −
2 + 2.17e−2 moil Tout Tout + 1.07e−3 Tout
Fig. 3. Example of a fraction of the matrix over one loop of the field
The value of the radiation in each element of the matrix depends on the following parameters: • The global incident solar radiation on the field. • The direction of the route followed by the passing cloud (the angle formed by this direction and the direction followed by the thermal fluid, the parallel being 0). • The velocity of the passing cloud (determined by the number of elements of the matrix supposed to be traveled by the cloud every 39 seconds, which is the sample time of the field). • The size of the cloud (a rectangular form is supposed, defined by the rows and columns that it covers). • The attenuation factor, which is the value that multiplies the radiation in the zones where the cloud is present. This value varies between 0 and 1 depending on the radiation which the cloud allows to arrive to the field, being 0 the case in which no radiation arrives to the field and 1 the case in which all the radiation arrives to it. Once these values are set, the program calculates for each collector the mean value of radiation of every element of the matrix related with it. This mean value is assigned to the variable I of (1).
(4)
(5)
The net electrical power produced by the field is the result of subtracting the power consumed by the pump to the power generated by the turbine. Therefore, to calculate the consumption of the pump we used the Darcy equations. Firstly, the Reynolds number and the Barr’s friction coefficient are computed by (6) and (7) respectively: Re = f = 0.25
ρf qd Af µ
1 log10(ϵr /3.7d + 5.74/Re0.9 )2
(6) (7)
where µ is the dynamic viscosity and ϵr is the relative rugosity. The Darcy equation for computing the pressure drop is given by (8): hpl = 9806.65
8f Lq 2 (P a) gπ 2 d5
(8)
where L is the loop length and d is the pipe diameter. The power consumption depends on the pump efficiency, oil flow and the pressure drop pd (9). Wpump =
qhpl (W ) ηpump
(9)
Finally, the net electrical power is calculated by (10). Wnet = W −
Wpump (kW ) 1000
(10)
3. CONTROL STRATEGIES
2.3 Power Cycle Model The power cycle model used in this paper (Fig. 2) consists of an economizer, a boiler and a super-heater followed by a turbine. The oil flow heated by the solar radiation concentrated by field collectors is firstly introduced into the super-heated where a steam stream is heated. Afterward, the oil is used to produce saturated steam in the boiler, which operates at a floating pressure. Finally the oil is sent to the economizer to preheat the water stream before being boiled. The super-heated steam is used to produce electrical power in a condensation turbine. This model was simulated using the software Engineering Equation Solver and then correlated with simulation results to get equations (4) and (5) in order to calculate the electrical power generated and the oil temperature 113
In this section two control strategies are presented. The feedforward with PI control strategy is the traditional one used in solar fields to keep constant the oil outlet temperature, whereas the Optimal control strategy is a new one proposed by the authors in order to maximize the electrical power generated and prevent the appearance of temperature peaks. 3.1 Feedforward with PI Control This control strategy consists of controlling the outlet temperature of the field by manipulating the total flow of the oil. This total flow is equally distributed among the loops. The control scheme can be seen in Fig. 4, where a series feedforward compensation is used.
Proceedings of the 20th IFAC World Congress 112 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
• Finally, with equations (6), (7), (8), (9) and (10) the net electrical power is calculated.
The feedforward controller provides compensation for variations in I and Tin calculating the desired flow of oil us using (11), where T0 is the outlet temperature to be maintained, P cp is a term that accounts for the product and quotient of characteristic magnitudes (areas, thermal capacities, etc. ), S is the effective surface, Hl is the global thermal losses coefficient, and Tm is the mean inlet-outlet temperature. Equation (11) comes from the concentrated parameters model of the field Camacho et al. (1997)Camacho et al. (2012)-Carmona (1985) considering steady state conditions. This equation can be approximated by (12), where u is the output of a PI controller (Kc = 1.09, τi = 150.28 s) placed before the feedforward controller in order to maintain the required steady state outlet temperature T0 due to the fact that exact compensation cannot be achieved with it. 1 (T0 − Tin )us = (n0 SI − Hl (Tm − Ta )) (11) P cp us =
3.15I − 0.204(u − 64.16) − 75.87 u − Tin
(12)
The radiation I used in (12) is the global incident solar radiation on the field which is calculated as the mean value of all elements of the matrix, and the variable Tin is the inlet temperature of the thermal fluid, calculated by (5). The constants that appear in the equation have been determined experimentally. 3.2 Optimal Control This control strategy is based on using an MPC controller, which uses models of the field and the power cycle, so that the controller could calculate the optimum value of oil outlet temperature which maximizes the electrical power generated, taking into account temperature and oil flow constraints. The control scheme can be seen in Fig.5.The dynamic optimization procedure may be expressed as the following algorithm: • All the variables needed by the field model are measured. • A simplified solar collector field model (1)-(2), which assumes that the pipe is only divided in 6 parts of 80 meters instead of the divisions of 1 meter for passive zones and 3 meters for the active zones in the model used for simulating the solar field, is used to calculate the outlet oil temperature of the field. The oil flow is the independent variable used by the optimizer. • With the calculated values of oil outlet temperature and mass oil flow, equations (4) and (5) are used to know the electrical power generated by the turbine and the inlet oil temperature. 114
Fig. 5. MPC controller
4. SIMULATION RESULTS This section shows the results obtained by simulations of both strategies explained in Section 3. These simulations have been carried out with the solar radiation curve shown in (Fig. 6) and using the models described in section 2. If we compared the feedforward with PI strategy with a fixed set point of 393◦ C against the optimal one, we can see that the feedforward with PI strategy presents the problem of temperature peaks in some loops (Fig. 7) whereas in the optimal strategy this situation does not happen (Fig. 8). The oscillations observed in Fig. 7 are due to use of a static feedforward with unmodelled dynamics; a problem that does not occur when the optimal controller is used (Fig. 8). In terms of electrical power (Fig. 9), it seems that during the central part of the day the feedforward strategy produces more than the optimal one, but at the cost of having temperature peaks. However, during the last part of the day, when the value of the incident solar radiation is low, the optimal strategy produces much more electrical power. Considering the entire operating day, the improvement achieved by the optimal strategy is around 2.15%. 900 Solar Radiation (W/m 2)
Fig. 4. Series feedforward controller
Therefore, the MPC has to maximize the value of net electrical power subject to restrictions in oil temperature (T ≤400◦ C) and oil flow (0.000133 m3 /s≤q≤0.00158 m3 /s) for each loop. The prediction and control horizons are equal to one, however, in future works, it is planned to increase these horizons incorporating predictions of the passing clouds. The optimization is carried out for each integration step by the function f mincon in MATLAB. The optimum value of oil flow would be then sent as the new set point of the flow controller, which manipulates the variable frequency drive, but in this simulation we are assuming that the flow is instantly changed.
800 700 600 500
0.4
0.6
0.8
1
1.2
1.4 Time (s)
Fig. 6. Incident solar radiation
1.6
1.8
2
2.2
2.4 ×104
410
400
400
390 Temperature (ºC)
Temperature (ºC)
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114
390 380 370 360
113
380 370 360
0.4
0.6
0.8
1
1.2
1.4 Time (s)
1.6
1.8
2
2.2
350
2.4 ×104
Fig. 7. Oil outlet temperature of the loops with a feedforward controller and a set point of 393◦ C
0.4
0.6
0.8
1
1.2
1.4 Time (s)
1.6
1.8
2
2.2
2.4 ×104
Fig. 10. Oil outlet temperature of the loops with a feedforward controller and a set point of 380◦ C
Electrical Power (kW)
3000
Temperature (ºC)
380 360
2000 1500 1000 500
340
0
320 300 0.4
0.6
0.8
1
1.2
1.4 Time (s)
1.6
1.8
2
2.2
2500 2000 1500 1000
0
Optimal Control Feedforward Control
0.4
0.6
0.8
1
1.2
1.4 Time (s)
1.6
0.4
0.6
0.8
1
1.2
1.4 Time (s)
1.6
1.8
2
2.2
2.4 ×104
5. CONCLUSION The main conclusion of this paper is, that to operate the field during a day with partial radiation at a constant oil outlet temperature is not the optimum way to do it and also can lead to the temperature peaks problem. Using the feedforward with PI strategy the only way to avoid this problem is to lower the oil outlet temperature set point, but in doing so, it also reduces the total amount of electrical power generated. For that reason the authors propose the use of the optimal strategy, which can prevent the temperature peaks problem and also maximizes the electrical power production, not only when there are passing clouds, but also when the value of the incident solar radiation is low.
3000
500
Feedforward Control Optimal Control
Fig. 11. Electrical power generated by the optimal strategy and the feedforward strategy with a set point of 380◦ C
2.4 ×104
Fig. 8. Oil outlet temperature of the loops with an optimal controller
Electrical Power (kW)
2500
1.8
2
2.2
2.4 ×104
ACKNOWLEDGEMENTS
Fig. 9. Electrical power generated by the optimal strategy and the feedforward strategy with a set point of 393◦ C
The authors wish to thank Professor Jo˜ao Lemos for his valuable comments and suggestions. REFERENCES
After seeing that with the feedforward with PI strategy with a set point of 393◦ C we could not avoid the problem of the appearance of temperature peaks, we tested the same strategy but with a lower set point equal to 380◦ C. Figure 10 shows that with this set point the temperature peaks do not appear, however, in terms of electrical power this new set point has worse results than the previous one (Fig. 11). Specifically, in this case the improvement achieved when compared with the optimal strategy is around 2.95%. 115
Abutayeh, M., Alazzam, A. and El-Khasawneh, B.(2014) Balancing heat transfer fluid flow in solar fields. Solar Energy, 105, 381-389. Bar˜ao, M., Lemos, J. and Silva, R. (2002). Reduced complexity adaptive nonlinear control of a distributed collector solar field. Journal of Process Control, 12-1, 131-141. Camacho, E. F., Berenguel, M. and Rubio, F. R. (1997). Advanced control of solar plants. Springer-Verlag, London.
Proceedings of the 20th IFAC World Congress 114 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
Camacho, E. F., Rubio, F. R., Berenguel, M. and Valenzuela, L. (2007). A survey on control schemes for distributed solar collector fields. Part I: Modeling and basic control approaches. Solar Energy, 81-10, 1240-1251. Camacho, E. F., Rubio, F. R., Berenguel, M. and Valenzuela, L. (2007). A survey on control schemes for distributed solar collector fields. Part II: Advanced control approaches. Solar Energy, 81-10, 1252-1272. Camacho, E. F., Berenguel, M., Rubio, F. R. and Mart´ınez, D. (2012). Control of solar energy systems. Springer-Verlag, London. Camacho, E. F. and Gallego, A. (2013). Optimal operation in solar trough plants: A case study. Solar Energy, 95, 106-117. Carmona, R. (1985). An´ alisis, modelado y control de un campo de colectores solares distribuidos con sistema de seguimiento en eje. Ph.D. Thesis. Cirre, C., Berenguel, M., Valenzuela, L. and Camacho, E. F. (2007). Feedback linearization control for a distributed solar collector field. Control Engineering Practice, 15-12, 1533-1544. Cirre, C., Berenguel, M., Valenzuela, L. and Klempous, R. (2009). Reference governor optimization and control of a distributed solar collector field. European Journal of Operational Research, 193, 709-717. Colmenar-Santos, A., Munuera-Prez, F., Tawfik, M. and Castro-Gil, M. (2014). A simple method for studying the effect of scattering of the performance parameters of parabolic trough collectors on the control of a solar field. Solar Energy, 99, 215-230. Gallego, A. and Camacho, E. F. (2012). Estimation of effective solar irradiation using an unscented kalman filter in a parabolic-trough field. Solar Energy, 86-12, 3512-3518. Lima, D., Normey-Rico, J. and Santos, T. (2016). Temperature control in a solar collector field using filtered dynamic matrix control. ISA Transactions, 62, 39-49. Lippke, F. (1995). Simulation of the part-load behavior of a 30 MWe SEGS plant. Report No. SAND95-1293, SNL, Albuquerque, NM, USA. Montes, M., Ab´anades, A., Mart´ınez-Val, J. and Vald´es, M. (2009). Solar multiple optimization for a solar-only thermal power plant, using oil as heat transfer fluid in the parabolic trough collectors. Solar Energy, 83-12, 2165-2176. Navas, S. J., Rubio, F. R., Ollero, P. and Ortega, M. G. (2016). Modeling and simulation of parabolic trough solar fields with partial radiation. XV European Control Conference, 31-36. Price, H., Lupfert, E., Kearney, D., Zarza, E., Cohen, G., Gee, R. and Mahoney, R. (2002). Advances in parabolic trough solar power technology. Solar Energy, 124-2, 109125. Rubio, F. R., Camacho, E. F. and Berenguel, M. (2014). Control de campos de colectores solares IberoAmerican Journal of Industrial Automation and Informatics (RIAI), 3-4, 26-45. Shinskey, F. (1978). Energy conservation through control. Academic Press. Smith, R. (2005). Chemical process design and integration. Wiley.
116
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IFAC PapersOnLine 50-1 (2017) 109–114
Optimum Optimum Control Control Optimum Control Solar Fields Solar Fields with with Solar Fields with ∗
of of Parabolic Parabolic Trough Trough ⋆ of Parabolic Trough Partial Radiation Partial Radiation ⋆⋆ Partial ∗∗Radiation ∗∗∗
Sergio J. Navas ∗ Francisco R. Rubio ∗∗ Pedro Ollero ∗∗∗ Sergio Sergio J. J. Navas Navas ∗ Francisco Francisco R. R. Rubio Rubio ∗∗ Pedro Pedro Ollero Ollero ∗∗∗ Sergio J. Navas ∗ Francisco R. Rubio ∗∗ Pedro Ollero ∗∗∗ ∗ ıa de Sistemas y Autom´ atica, Universidad ∗ Departamento de Ingenier´ ∗ Departamento de Ingenier´ ıa Sistemas a de Ingenier´ ıa de de(e-mail:[email protected]). Sistemas yy Autom´ Autom´ atica, tica, Universidad Universidad de Sevilla, Spain ∗ Departamento de Ingenier´ ıa de(e-mail:[email protected]). Sistemas y Autom´ atica, Universidad de Sevilla, Spain ∗∗Departamento de Sevilla, Spain (e-mail:[email protected]). Departamento de Ingenier´ ıa de Sistemas y Autom´ a tica, Universidad ∗∗ de de Sevilla, Spain (e-mail:[email protected]). ∗∗ Departamento Ingenier´ ıa Sistemas yy Autom´ a Ingenier´ ıa de de(e-mail: Sistemas Autom´ atica, tica, Universidad Universidad Spain [email protected]) ∗∗ DepartamentodedeSevilla, deSevilla, Ingenier´ ıa de(e-mail: Sistemas y Autom´ atica, Universidad Spain [email protected]) ∗∗∗Departamentode de Sevilla, Spain (e-mail: [email protected]) Departamento de Ingenier´ ıa Qu´ ımica y Ambiental, Universidad de ∗∗∗ de de Sevilla, Spain (e-mail: [email protected]) ∗∗∗ Departamento ıa Qu´ de Ingenier´ Ingenier´ ıa(e-mail: Qu´ımica ı[email protected]) y Ambiental, Ambiental, Universidad Universidad de de Spain ∗∗∗ DepartamentoSevilla, DepartamentoSevilla, de Ingenier´ Qu´ı[email protected]) y Ambiental, Universidad de Spainıa(e-mail: (e-mail: Sevilla, Spain [email protected]) Sevilla, Spain (e-mail: [email protected]) Abstract: This paper describes the main problems of operating parabolic trough solar fields Abstract: describes the main problems of trough solar Abstract: This paper describes the An mainoptimal problems of operating operating parabolic trough solar fields fields during daysThis withpaper partial radiation. control strategyparabolic is proposed to solve these Abstract: This paper describes the An main problems of operating parabolic trough solar fields during with partial control strategy is to these during days days with partial radiation. radiation. An optimal optimal control strategy is proposed proposed toPIsolve solve these problems and it is assessed against a classical one, which uses a feedforward and a controller during days with partial radiation. An optimal control strategy is proposed to solve these problems and it is assessed against a classical one, which uses a feedforward and a PI controller problems and set it is point assessed against a classical one, which uses a feedforward and a PI controller with a fixed of oil outlet temperature. Some simulations have been made using problems and it is assessed against a classical one, which uses a feedforward and a PI controller with set outlet Some simulations made using with aa fixed fixed set point point of of oil oil using outlet temperature. temperature. Some simulations have been made using MATLAB to demonstrate optimal control strategy better have resultsbeen can be achieved. with a fixed set point ofthat oil outletthe temperature. Some simulations have been made using MATLAB MATLAB to to demonstrate demonstrate that that using using the the optimal optimal control control strategy strategy better better results results can can be be achieved. achieved. MATLAB to (International demonstrate Federation that usingofthe optimalControl) control Hosting strategy results can be achieved. © 2017, IFAC Automatic bybetter Elsevier Ltd. All rights reserved. Keywords: Solar, Control, Optimization, Parabolic Trough, Simulation, Partial Radiation Keywords: Solar, Solar, Control, Control, Optimization, Optimization, Parabolic Parabolic Trough, Trough, Simulation, Simulation, Partial Partial Radiation Radiation Keywords: Keywords: Solar, Control, Optimization, Parabolic Trough, Simulation, Partial Radiation 1. INTRODUCTION On the other hand, using a PI with a feedforward controller 1. INTRODUCTION INTRODUCTION On other PI aa feedforward controller 1. On the the other hand, hand, using using PI with with feedforward controller that manipulates oil aaaflow to keep constant the outlet 1. INTRODUCTION On the other hand,the using PI with a feedforward controller that manipulates the oil flow to keep constant the outlet that manipulates the oil flow to keep constant the outlet of the field, like in Camacho et al. (1997)The main technologies for converting solar energy into temperature that manipulates thefield, oil flow to keep constant the(1997)outlet temperature of the like in Camacho et al. The main technologies for converting solar energy into temperature of the field, like in Camacho et al. (1997)et al. (2012)-Carmona (1985), while a cloud is The main are technologies for (PV) converting solar energy solar into Camacho electricity photovoltaic and concentrated temperature of the field, like in Camacho et al. (1997)The main technologies for converting solar energy into Camacho et al. (2012)-Carmona (1985), while a cloud is electricity(CST). are photovoltaic photovoltaic (PV) and and concentrated solar passing Camacho et al. (2012)-Carmona (1985), while a cloud is through the field may provoke temperature peaks electricity are (PV) concentrated solar thermal Parabolic trough, solar towers, Fresnel Camacho et al. (2012)-Carmona (1985), while a cloud is electricity are photovoltaic (PV) and concentrated solar passing through the field may provoke temperature peaks thermal (CST). Parabolic trough, solar towers, Fresnel passing through the field may provoke temperature peaks in some loops. This situation is due to the fact that when thermal (CST). Parabolic trough, solar towers, Fresnel collector and solar dishes are the most used technolopassing through the field may provoke temperature peaks thermal (CST). Parabolic trough, towers, Fresnel in some due to when collector and solar solar dishes are the solar most used technolotechnolosome loops. This situation iswill duedecrease to the the fact fact that when the cloudloops. passesThis the situation controlleris the that oil flow in collector and dishes the most used gies for concentrating solar are energy. This paper focus on in in some loops. This situation iswill duedecrease to the fact that when collector and solar dishes are the most used technolothe cloud passes the controller the oil flow in gies for concentrating solar energy. This paper focus on the cloud passes the controller will decrease the oil flow in to keep the outlet temperature constant, however, gies for concentrating solar energy. This paper focus on order parabolic trough solar fields, which consist of a collector the cloud passes the controller will decrease the oil flow in gies for concentrating solar energy. This paper focus on order to keep the outlet temperature constant, however, parabolic trough solar fields, which consist of a collector order to keep the outlet temperature constant, however, in the loops that are not covered by the cloud, the solar parabolic trough solar fields, which consist of a collector field (Fig. trough 1), a power and auxiliary elements such as order to keepthat the are outlet temperature constant, however, parabolic solarcycle fields, which consist of a collector in the loops not covered by the cloud, the solar field (Fig. 1), a power cycle and auxiliary elements such as in the loops thatreduced, are not covered thetemperature cloud, the solar is not so that by their will field (Fig. 1), aand power cycleThe andsolar auxiliary elements such as radiation pumps, pipes valves. collector field collects the loops thatreduced, are not covered by the cloud, the solar field (Fig. 1), aand power cycleThe andsolar auxiliary elements such as in radiation is so their will pumps, pipes valves. collector field collects collects radiation is not not reduced, so that that limit. their temperature temperature will be increased above the security If this situation pumps, pipes and valves. The solaracollector field solar radiation and focuses it onto tube in which a heat radiation is not reduced, so that limit. their temperature will pumps, pipes and valves. The solaracollector field collects be increased above the security If this situation solar radiation and focuses it onto tube in which a heat be increased above the security limit. If this situation the collectors aresecurity programmed toIfget outsituation of focus solar radiation and focuses it onto tube in which heat transfer fluid, usually synthetic oil,aa circulates. Theaa oil is happens be increased above the limit. this solar radiation and focuses it onto tube in which heat happens the collectors are programmed to get out of focus transferup fluid, usually synthetic oil, circulates. The oil is is to happens the are programmed to involve get out aofloss focus prevent oilcollectors degradation, but that would of transfer fluid, synthetic circulates. oil heated andusually then used by theoil, power cycle toThe produce the collectors are programmed to involve get out aofloss focus transfer fluid, usually synthetic circulates. oil is happens to oil degradation, but would heated up up andmeans then of used by the theoil, power cycle to toThe produce to prevent prevent oil degradation, but that that would involve a loss of of energy and it is not considered in this paper as a possible heated and then used by power cycle produce electricity by a turbine. prevent but that would involve a loss of heated up by andmeans then of usedturbine. by the power cycle to produce to energy andoil it degradation, is not not considered considered in this this paper as aa possible possible electricity energy and it is in paper as solution. electricity by means of aa turbine. energy and it is not considered in this paper as a possible electricity by means of a turbine. solution. solution. The main goal of a parabolic trough solar field is to solution. The main main goal of aa parabolic parabolic trough solar to field is to to In this paper the effect of the solar radiation on the outlet The of trough solar field is collect the goal maximum solar energy in order produce The main goal of a parabolic trough solar to field is to In of solar the collect the maximum solar energy in order produce In this this paper paper the the effect of the the solar radiation on the outlet outlet was effect studied with a radiation complete on power cycle collect maximum solarasenergy in order to produce as muchthe electrical power possible. Normally, this is temperature In this paper the effect of the solar radiation on the outlet collect the maximum solar energy in order to produce temperature was studied with a complete power cycle as much electrical power as possible. Normally, this is temperature was studied with a complete power cycle model (Fig. 2) reduced to a correlation that relates the as much electrical power as possible. Normally, this is achieved keepingpower the outlet temperature of the field temperature was studiedto with a complete power cycle as much by electrical as possible. Normally, this is model (Fig. 2) reduced a correlation that relates the achieved by keeping the outlet temperature of the field model (Fig. 2) reduced to abycorrelation that relates the ◦ electrical power generated the condensation turbine achieved bymaximum keeping the outlet value, temperature of the field around the allowable that is 400 C, due model (Fig. 2) reduced to abycorrelation that relates the ◦ achieved bymaximum keeping the outlet value, temperature of the electrical power generated the condensation turbine ◦ C, field around the allowable that is 400 due electrical power generated by the condensation turbine the mass flow and outlet temperature of the oil. In around the maximum allowable value, that iswe400 due with to oil degradation. However, in this paper, will ◦ C,show electrical power generated by the condensation turbine around the maximum allowable value, that is 400 C, due with the mass flow and outlet temperature of the oil. to oil degradation. However, in this paper, we will with the mass flow and outletit temperature of the oil. In In Camacho and Gallego (2013) is used a similar approach to oilthis degradation. However, in thisdoes paper, we will show show that way to operate the field not produce the with the mass flow and outlet temperature of the oil. In to oilthis degradation. However, in thisdoes paper, we will show Camacho and Gallego (2013) it is used aa similar approach that way to operate the field not produce the Camacho and Gallego (2013) it is used similar approach but they use a correlation that only depends on the outlet that this way to operate the field does not produce the best results of electrical power generated. This problem Camacho and Gallego (2013) it is used a similar approach that results this wayof to operate power the field does notThis produce the but but they they use use aa correlation correlation that only only depends depends on the the outlet best generated. that on outlet implies efficiency higher than the best been results of electrical electrical power generated. problem has studied before in Lippke (1995), This whereproblem it was temperature, but they use athat correlation that onlyresults depends on the outlet best results of electrical power generated. This problem temperature, that implies efficiency results higher than the has been studied before in Lippke (1995), where it was temperature, that implies efficiency results higher than the found in the literature Lippke (1995); in addition has been studied before in strategy Lippke (1995), where it was ones suggested that the optimum is based on adapting that implies efficiency results higher than the has been studied before in strategy Lippke (1995), where it was temperature, ones found in the literature Lippke (1995); in addition the suggested that the optimum is based on adapting ones found in the literature Lippke (1995); in addition the simulations made in this paper were carried out taking suggested that the optimum strategy is based on adapting the fluid outlet temperature the incident solar found inmade the literature Lippke (1995); in addition the suggested that the optimumto strategy is based onradiation, adapting ones simulations in this paper were carried out taking the fluid outlet temperature to the incident solar radiation, simulations made in this paper were carried out taking into account a model of the entire field, not assuming the fluid outlet temperature to the incident solar radiation, keeping the constant the superheating temperature of the simulations made in this paper were carried out taking the fluid the outlet temperature to the incident solar radiation, account aa model the entire field, not assuming keeping constant the temperature of into account model of loop the is entire field, than not the assuming that the behavior of oneof the same other keepingitthe constant the superheating superheating temperature of the the into steam; was also studied in Montes et al. (2009) where account a model of loop the is entire field, than not the assuming keeping the constant the superheating temperature of the into that the behavior of one the same other steam; it was also studied in Montes et al. (2009) where that the behavior of one loop is the same than the other ◦ ones. Therefore, the authors propose that using an optimal it was alsotemperature studied in Montes et (393 al. (2009) where asteam; constant outlet was used C). Finally, that the behavior of one loop is the same than the other ◦ steam; it was also studied in Montes et al. (2009) where ones. Therefore, the authors propose that using an optimal ◦ aa constant outlet temperature was used (393 C). Finally, ones. Therefore, the authors propose that using an optimal controller with constraints can prevent the appearance of constant outlet temperature was used (393 C). Finally, more recent study was carried out in Camacho and ones. ◦ Therefore, the authorscan propose thatthe using an optimal a constant outlet temperature was used (393 C). Finally, controller with constraints prevent appearance of aaGallego more recent study was carried out in Camacho and controller with constraints can prevent the appearance of temperature peaks and also maximize the electrical power more (2013) recent where study itwas carried out in Camacho and was carried proposed to in change the outlet with constraints can preventthe theelectrical appearance of a more (2013) recent where study itwas out Camacho and controller temperature peaks and also maximize power Gallego was proposed to change the outlet temperature peaks and also maximize the electrical power generated by the field depending on the value of solar Gallego (2013) where itaccording was proposed to value changeofthe outlet temperature set point to the the solar temperature peaks and also maximize the electrical power Gallego (2013) where it was proposed to change the outlet generated by the field depending on the value of solar temperature the field depending on the value of solar radiation. by temperature set set point point according according to to the the value value of of the the solar solar generated radiation. by the field depending on the value of solar temperature set point according to the value of the solar generated radiation. radiation. radiation. radiation. radiation. radiation. The paper is organized as follows: Section 2 describes the ⋆ This work was supported by the projects DPI2013-44135-R and The is as follows: Section 22 describes the The paper paper is organized organized as passing follows: clouds Sectionand describes the ⋆ models of the solar field, power cycle This work was supported by the projects DPI2013-44135-R and ⋆ The paper is organized as passing follows: clouds Sectionand 2 describes the This work was supported by the projects DPI2013-44135-R and DPI2015-70973-R granted by the Spanish Ministry of Science models of the solar field, power cycle ⋆ models ofsimulation the solar field, passing cloudsIIIand power cycle This work was supported bythe theSpanish projectsMinistry DPI2013-44135-R used for purposes. Section describes both DPI2015-70973-R granted by of Science and DPI2015-70973-R granted by the Spanish Ministry of Science and models of the solar field, passing clouds and power cycle Innovation. used for for simulation simulation purposes. purposes. Section Section III III describes describes both both DPI2015-70973-R granted by the Spanish Ministry of Science and used Innovation. Innovation. used for simulation purposes. Section III describes both Innovation.
Copyright © 2017, 2017 IFAC 111 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2017 IFAC 111 Copyright ©under 2017 responsibility IFAC 111Control. Peer review of International Federation of Automatic Copyright © 2017 IFAC 111 10.1016/j.ifacol.2017.08.019
Proceedings of the 20th IFAC World Congress 110 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
control strategies tested: the feedforward with a PI control and the optimum control. Section IV shows the results obtained by simulations made in MATLAB. Finally, the paper draws to a close with some concluding remarks.
differential equations describing the energy balance: Active zones
ρm Cm Am
∂Tm = In0 G − Hl G(Tm − Ta ) − ∂t LHt (Tm − Tf )
(1)
Fluid element ρf Cf Af
∂Tf ∂Tf + ρf Cf q˙ = LHt (Tm − Tf ) ∂t ∂x
(2)
Passive zones Fig. 1. ACUREX distributed solar collector field ρm Cm Am
∂Tm = −Hp (Tm − Ta ) − LHt (Tm − Tf ) ∂t
(3)
where the sub-index m refers to metal and f refers to the fluid. The model parameters and their units are shown in table 1. Table 1. Solar field model parameters description
Fig. 2. Diagram of the solar field connected with the power cycle
Symbol t x ρ C A T q˙ I n0 G Ta Hl
2. SYSTEM MODELING
Ht
The model of each of the parts which have been used to simulate the operation of a solar field during the days with partial covering is presented. These parts are: the solar collector field, the passage of the clouds and the power cycle.
Hp
2.1 Solar Collector Field Model In this subsection, the mathematical model of a parabolic trough solar field is presented. This model is the same used in Navas et al. (2016) which is at the same time a slight modification of the model proposed by Camacho et al. (1997)-Camacho et al. (2012)-Carmona (1985) for the ACUREX field (Fig. 1). Basically, this model can be used to simulate parabolic trough solar fields by selecting parameters like the number of active (the parts where the solar radiation reaches the tube) and passive (joints and other parts not reached by concentrated solar radiation) zones, length of each zone, or collector aperture. The solar field simulated in this paper is supposed to be on the site of the Escuela Superior de Ingenier´ıa de Sevilla. It is composed of 24 loops and has dimensions of 144x240 m2 . Each loop is modeled by the following system of partial 112
L
Description Time Space Density Specific heat capacity Cross sectional area Temperature Oil flow rate Solar radiation Optical efficiency Collector aperture Ambient Temperature Global coefficient of thermal losses for active zones Coefficient of heat transmission metal-fluid Global coefficient of thermal losses for passive zones Length of pipe line
Units s m Kg/m3 J/(K kg) m2 ◦C m3 /s W/m2 Unit-less M ◦C W/(m2 ◦ C) W/(m2 ◦ C) W/(m2 ◦ C) m
The density ρ, specific heat C and coefficient of thermal loss Hl depend on fluid temperature. The coefficient of heat transmission Ht depends on temperature and oil flow. The incident solar radiation I depends on hourly angle, solar hour, declination, Julianne day, local latitude and collector dimensions Camacho et al. (1997)-Camacho et al. (2012)-Carmona (1985). In order to solve this system of partial differential equations, a two stage finite difference equation has been programmed, considering each segment of 1 m for the passive zones and of 3 m for the active zones and solving (1)-(2)-(3). 2.2 Modeling of the Passing Clouds The modeling of the passing clouds is necessary to know how the radiation of the sun is distributed throughout the field. This can be achieved creating a matrix which represents the whole field extension. Each element of the matrix is assigned the value of the incident solar radiation
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114
on that section at each time. The solar field has dimensions of 144x240 m2 , so if we divide the matrix in elements of 3x3 meters we need a 48x80 matrix. The matrix is then put over the field in such a way that each element contains a fraction of an active or passive element. Fig.3 shows the fraction of the whole matrix that covers one loop of a generic field.
111
returning to the field respectively. This simplification was necessary to reduce the simulation time and the error is around 1%. In addition the dynamic of the cycle was assumed to be like a first order model with a time constant of 100 seconds. W = 8.23e3 − 49.96moil − 2.70m2oil −
2 + 5.38e−1 moil Tout 47.15Tout + 6.75e−2 Tout
Tin = 3.40e2 + 1.78moil − 1.55e−1 m2oil −
2 + 2.17e−2 moil Tout Tout + 1.07e−3 Tout
Fig. 3. Example of a fraction of the matrix over one loop of the field
The value of the radiation in each element of the matrix depends on the following parameters: • The global incident solar radiation on the field. • The direction of the route followed by the passing cloud (the angle formed by this direction and the direction followed by the thermal fluid, the parallel being 0). • The velocity of the passing cloud (determined by the number of elements of the matrix supposed to be traveled by the cloud every 39 seconds, which is the sample time of the field). • The size of the cloud (a rectangular form is supposed, defined by the rows and columns that it covers). • The attenuation factor, which is the value that multiplies the radiation in the zones where the cloud is present. This value varies between 0 and 1 depending on the radiation which the cloud allows to arrive to the field, being 0 the case in which no radiation arrives to the field and 1 the case in which all the radiation arrives to it. Once these values are set, the program calculates for each collector the mean value of radiation of every element of the matrix related with it. This mean value is assigned to the variable I of (1).
(4)
(5)
The net electrical power produced by the field is the result of subtracting the power consumed by the pump to the power generated by the turbine. Therefore, to calculate the consumption of the pump we used the Darcy equations. Firstly, the Reynolds number and the Barr’s friction coefficient are computed by (6) and (7) respectively: Re = f = 0.25
ρf qd Af µ
1 log10(ϵr /3.7d + 5.74/Re0.9 )2
(6) (7)
where µ is the dynamic viscosity and ϵr is the relative rugosity. The Darcy equation for computing the pressure drop is given by (8): hpl = 9806.65
8f Lq 2 (P a) gπ 2 d5
(8)
where L is the loop length and d is the pipe diameter. The power consumption depends on the pump efficiency, oil flow and the pressure drop pd (9). Wpump =
qhpl (W ) ηpump
(9)
Finally, the net electrical power is calculated by (10). Wnet = W −
Wpump (kW ) 1000
(10)
3. CONTROL STRATEGIES
2.3 Power Cycle Model The power cycle model used in this paper (Fig. 2) consists of an economizer, a boiler and a super-heater followed by a turbine. The oil flow heated by the solar radiation concentrated by field collectors is firstly introduced into the super-heated where a steam stream is heated. Afterward, the oil is used to produce saturated steam in the boiler, which operates at a floating pressure. Finally the oil is sent to the economizer to preheat the water stream before being boiled. The super-heated steam is used to produce electrical power in a condensation turbine. This model was simulated using the software Engineering Equation Solver and then correlated with simulation results to get equations (4) and (5) in order to calculate the electrical power generated and the oil temperature 113
In this section two control strategies are presented. The feedforward with PI control strategy is the traditional one used in solar fields to keep constant the oil outlet temperature, whereas the Optimal control strategy is a new one proposed by the authors in order to maximize the electrical power generated and prevent the appearance of temperature peaks. 3.1 Feedforward with PI Control This control strategy consists of controlling the outlet temperature of the field by manipulating the total flow of the oil. This total flow is equally distributed among the loops. The control scheme can be seen in Fig. 4, where a series feedforward compensation is used.
Proceedings of the 20th IFAC World Congress 112 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
• Finally, with equations (6), (7), (8), (9) and (10) the net electrical power is calculated.
The feedforward controller provides compensation for variations in I and Tin calculating the desired flow of oil us using (11), where T0 is the outlet temperature to be maintained, P cp is a term that accounts for the product and quotient of characteristic magnitudes (areas, thermal capacities, etc. ), S is the effective surface, Hl is the global thermal losses coefficient, and Tm is the mean inlet-outlet temperature. Equation (11) comes from the concentrated parameters model of the field Camacho et al. (1997)Camacho et al. (2012)-Carmona (1985) considering steady state conditions. This equation can be approximated by (12), where u is the output of a PI controller (Kc = 1.09, τi = 150.28 s) placed before the feedforward controller in order to maintain the required steady state outlet temperature T0 due to the fact that exact compensation cannot be achieved with it. 1 (T0 − Tin )us = (n0 SI − Hl (Tm − Ta )) (11) P cp us =
3.15I − 0.204(u − 64.16) − 75.87 u − Tin
(12)
The radiation I used in (12) is the global incident solar radiation on the field which is calculated as the mean value of all elements of the matrix, and the variable Tin is the inlet temperature of the thermal fluid, calculated by (5). The constants that appear in the equation have been determined experimentally. 3.2 Optimal Control This control strategy is based on using an MPC controller, which uses models of the field and the power cycle, so that the controller could calculate the optimum value of oil outlet temperature which maximizes the electrical power generated, taking into account temperature and oil flow constraints. The control scheme can be seen in Fig.5.The dynamic optimization procedure may be expressed as the following algorithm: • All the variables needed by the field model are measured. • A simplified solar collector field model (1)-(2), which assumes that the pipe is only divided in 6 parts of 80 meters instead of the divisions of 1 meter for passive zones and 3 meters for the active zones in the model used for simulating the solar field, is used to calculate the outlet oil temperature of the field. The oil flow is the independent variable used by the optimizer. • With the calculated values of oil outlet temperature and mass oil flow, equations (4) and (5) are used to know the electrical power generated by the turbine and the inlet oil temperature. 114
Fig. 5. MPC controller
4. SIMULATION RESULTS This section shows the results obtained by simulations of both strategies explained in Section 3. These simulations have been carried out with the solar radiation curve shown in (Fig. 6) and using the models described in section 2. If we compared the feedforward with PI strategy with a fixed set point of 393◦ C against the optimal one, we can see that the feedforward with PI strategy presents the problem of temperature peaks in some loops (Fig. 7) whereas in the optimal strategy this situation does not happen (Fig. 8). The oscillations observed in Fig. 7 are due to use of a static feedforward with unmodelled dynamics; a problem that does not occur when the optimal controller is used (Fig. 8). In terms of electrical power (Fig. 9), it seems that during the central part of the day the feedforward strategy produces more than the optimal one, but at the cost of having temperature peaks. However, during the last part of the day, when the value of the incident solar radiation is low, the optimal strategy produces much more electrical power. Considering the entire operating day, the improvement achieved by the optimal strategy is around 2.15%. 900 Solar Radiation (W/m 2)
Fig. 4. Series feedforward controller
Therefore, the MPC has to maximize the value of net electrical power subject to restrictions in oil temperature (T ≤400◦ C) and oil flow (0.000133 m3 /s≤q≤0.00158 m3 /s) for each loop. The prediction and control horizons are equal to one, however, in future works, it is planned to increase these horizons incorporating predictions of the passing clouds. The optimization is carried out for each integration step by the function f mincon in MATLAB. The optimum value of oil flow would be then sent as the new set point of the flow controller, which manipulates the variable frequency drive, but in this simulation we are assuming that the flow is instantly changed.
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Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114
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5. CONCLUSION The main conclusion of this paper is, that to operate the field during a day with partial radiation at a constant oil outlet temperature is not the optimum way to do it and also can lead to the temperature peaks problem. Using the feedforward with PI strategy the only way to avoid this problem is to lower the oil outlet temperature set point, but in doing so, it also reduces the total amount of electrical power generated. For that reason the authors propose the use of the optimal strategy, which can prevent the temperature peaks problem and also maximizes the electrical power production, not only when there are passing clouds, but also when the value of the incident solar radiation is low.
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Fig. 11. Electrical power generated by the optimal strategy and the feedforward strategy with a set point of 380◦ C
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ACKNOWLEDGEMENTS
Fig. 9. Electrical power generated by the optimal strategy and the feedforward strategy with a set point of 393◦ C
The authors wish to thank Professor Jo˜ao Lemos for his valuable comments and suggestions. REFERENCES
After seeing that with the feedforward with PI strategy with a set point of 393◦ C we could not avoid the problem of the appearance of temperature peaks, we tested the same strategy but with a lower set point equal to 380◦ C. Figure 10 shows that with this set point the temperature peaks do not appear, however, in terms of electrical power this new set point has worse results than the previous one (Fig. 11). Specifically, in this case the improvement achieved when compared with the optimal strategy is around 2.95%. 115
Abutayeh, M., Alazzam, A. and El-Khasawneh, B.(2014) Balancing heat transfer fluid flow in solar fields. Solar Energy, 105, 381-389. Bar˜ao, M., Lemos, J. and Silva, R. (2002). Reduced complexity adaptive nonlinear control of a distributed collector solar field. Journal of Process Control, 12-1, 131-141. Camacho, E. F., Berenguel, M. and Rubio, F. R. (1997). Advanced control of solar plants. Springer-Verlag, London.
Proceedings of the 20th IFAC World Congress 114 Sergio J. Navas et al. / IFAC PapersOnLine 50-1 (2017) 109–114 Toulouse, France, July 9-14, 2017
Camacho, E. F., Rubio, F. R., Berenguel, M. and Valenzuela, L. (2007). A survey on control schemes for distributed solar collector fields. Part I: Modeling and basic control approaches. Solar Energy, 81-10, 1240-1251. Camacho, E. F., Rubio, F. R., Berenguel, M. and Valenzuela, L. (2007). A survey on control schemes for distributed solar collector fields. Part II: Advanced control approaches. Solar Energy, 81-10, 1252-1272. Camacho, E. F., Berenguel, M., Rubio, F. R. and Mart´ınez, D. (2012). Control of solar energy systems. Springer-Verlag, London. Camacho, E. F. and Gallego, A. (2013). Optimal operation in solar trough plants: A case study. Solar Energy, 95, 106-117. Carmona, R. (1985). An´ alisis, modelado y control de un campo de colectores solares distribuidos con sistema de seguimiento en eje. Ph.D. Thesis. Cirre, C., Berenguel, M., Valenzuela, L. and Camacho, E. F. (2007). Feedback linearization control for a distributed solar collector field. Control Engineering Practice, 15-12, 1533-1544. Cirre, C., Berenguel, M., Valenzuela, L. and Klempous, R. (2009). Reference governor optimization and control of a distributed solar collector field. European Journal of Operational Research, 193, 709-717. Colmenar-Santos, A., Munuera-Prez, F., Tawfik, M. and Castro-Gil, M. (2014). A simple method for studying the effect of scattering of the performance parameters of parabolic trough collectors on the control of a solar field. Solar Energy, 99, 215-230. Gallego, A. and Camacho, E. F. (2012). Estimation of effective solar irradiation using an unscented kalman filter in a parabolic-trough field. Solar Energy, 86-12, 3512-3518. Lima, D., Normey-Rico, J. and Santos, T. (2016). Temperature control in a solar collector field using filtered dynamic matrix control. ISA Transactions, 62, 39-49. Lippke, F. (1995). Simulation of the part-load behavior of a 30 MWe SEGS plant. Report No. SAND95-1293, SNL, Albuquerque, NM, USA. Montes, M., Ab´anades, A., Mart´ınez-Val, J. and Vald´es, M. (2009). Solar multiple optimization for a solar-only thermal power plant, using oil as heat transfer fluid in the parabolic trough collectors. Solar Energy, 83-12, 2165-2176. Navas, S. J., Rubio, F. R., Ollero, P. and Ortega, M. G. (2016). Modeling and simulation of parabolic trough solar fields with partial radiation. XV European Control Conference, 31-36. Price, H., Lupfert, E., Kearney, D., Zarza, E., Cohen, G., Gee, R. and Mahoney, R. (2002). Advances in parabolic trough solar power technology. Solar Energy, 124-2, 109125. Rubio, F. R., Camacho, E. F. and Berenguel, M. (2014). Control de campos de colectores solares IberoAmerican Journal of Industrial Automation and Informatics (RIAI), 3-4, 26-45. Shinskey, F. (1978). Energy conservation through control. Academic Press. Smith, R. (2005). Chemical process design and integration. Wiley.
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