Small-capacity ( <200 kW el) concentrated solar power plants has been recognized as a promising technology for micro power applications. In particular, parabolic through collectors have been identiﬁed as the most promising focusing technology. In this context, physics-based dynamic model of parabolic through constitutes a signiﬁcant tool for the further development of the technology, allowing to evaluate and optimize response times during transients, or to implement and test innovative control strategies. In this contribution, the dynamic model of a parabolic trough line t based on the ThermoCycle Modelica library is validated against steady-state and transient experimental results from the parabolic through test loop available at the Plataforma Solar de Almer ´ıa, Spain. The simulation results are in good agreement with the measurements, both in steady-state and in transient conditions. The validated model is readily usable to investigate demanding dynamics-based problems for low capacity solar power systems. Keywords: Parabolic through collectors, Dynamic validation, Modelica 1. Introduction Recent studies have envisaged the potential of small-capacity ( <200 kW el) concentrated solar power (CSP) plants in case the future distributed energy scenario is considered [9, 24]. The ﬁrst documented CSP systems date back to the end of the 10thcentury [7]. Several CSP systems were developed and tested during the years, and the ﬁrst commercial plants were built in the 80’s in California, USA [20]. The main collector technologies are point-focussing parabolic dishes, solar towers, and line-focussing parabolic troughs, vacuum tube or non-concentrating ﬂat plate collectors [33]. Non or low-concentrating conﬁgurations are particularly attractive for small-scale power units, as the lower invest- ment costs may lead to economic viability. In particular, parabolic through collectors (PTCs) are suited to supply low or medium temperature thermal energy to generate electricity in combination with low-temperature organic Rankine cycle (ORC) engines [3, 32]. Corresponding author Email address: adesideri@ulg.ac.be (Adriano Desideri) Preprint submitted to SolarEnergy September 19, 2018 Nomenclature Acronyms CSP Concentrated solar power PTC Parabolic through collectors ORC Organic Rankine cycle HTF Heat transfer ﬂuid DSG Direct steam generation FV Finite volume MB Moving boundary PSA Plataforma solar de Almer ´ıa HCE Heat collection element CV Control volume TT Temperature transmittance DNI Direct normal irradiation ETC EuroTrough collector SF Solar ﬁeld EI Exogenous inputs IAM Incidence angle modiﬁer PCE Percentage computational e ort Subscripts su supply ex exhaust conv convection amb ambientsol solar rad radiation ext external int internal meas measured el electrical wf working ﬂuid Symbols p pressure (bar) T temperature (C) Vs volume (m3) ˙q heat ﬂux (kW.m2) M mass (kg) h speciﬁc enthalpy (kJ.kg1)  density (kg m3) ˙m mass ﬂow (kg.s1) Cp speciﬁc heat capacity (kJ.(kg.K)1) A area (m2) D diameter (m) N number of nodes (-) ¯" relative error (%) E energy (kJ) PTCs are by far the most mature solar concentrating technologies, as demonstrated commercially [14]. A PTC is a line-focusing parabola-shaped mirror which concentrates direct solar radiation on the absorber tube, located in the parabola’s focal line. An heat transfer ﬂuid (HTF) is pumped through the absorber tube acquiring thermal energy from the concentrated solar radiation. Parabolic trough solar thermal power plants commonly use thermal oil as HTF. This technology has been continuously improved since its ﬁrst commercial implementation [8]. In recent years, water has been tested as HTF in the collectors. The technology, called Direct Steam Generation (DSG), generates superheated steam directly from the collectors and presents important challenges due to phase changes in the HTF [6]. Due to the non-constant nature characterizing the direct solar irradiation, speciﬁc control strategies ensuring safe 2 and optimal operation of the CSP systems in any conditions are required. Before a control system can be designed, the dynamic behaviour of the CSP plant must be investigated. To this end, it is fundamental to study the transient related to the solar ﬁeld. In the literature, dynamic process models of PTCs are mainly one-dimensional in ﬂow direction and date back to the late ’70s. The Finite V olume (FV) method is the preferred approach for the discretization of the absorber tube. Nevertheless, when DSG is considered Moving Boundary (MB) models can be also applied. Ray [26] presented in 1980 a non-linear dynamic model of a parabolic trough unit for DSG. The FV modelling approach was adopted and the transient response of the model under di erent step disturbances was presented as typ- ical results. Hirsch et al. [12, 30] developed one of the ﬁrst Modelica PTC models. A FV based solar collector model of a DSG plant was introduced together with a preliminary validation based on the ﬁrst experimental results of the DISS facility at the Plataforma Solar de Almer ´ıa (PSA), Spain. More recently, a tri-dimensional non-linear dynamic thermohydraulic model of a PTC was also developed in Modelica and coupled to a solar industrial process heat plant modelled in TRNSYS [29]. A DSG PTC model was validated against results from the DISS facility, in [22], showing a good agreement. Several dynamic models of CSP plants were developed in Modelica based on the ThermoSysPro library [19]. A full scale dynamic model of a parabolic trough power plant with a thermal storage system is presented in [2]; simulation results are compared to experimental data from the real power plant. This work is extended in [1] including the power block and all the automation processes, simulated results are compared to measured data from an existing solar power plant. A simulation model for DSG in PTCs is developed in TRNSYS [5], results are validated with real data at the DISS facility. A thermal hydraulic RELAP5 DSG PTC model was validated against the DISS facility in [28], a new experimental correlation for heat losses was also provided. A non-linear dynamic model of once-through DSG PTCs was developed in [18], transfer functions of outlet ﬂuid temperature and mass ﬂow rate were also derived. The present work focuses on the steady-state and dynamic validation of a parabolic through collector model included in the open-source ThermoCycle Modelica library, for the modelling of small thermo-hydraulic system [25]. The main contribution consists in a through validation of the PTC model against experimental data collected at the PTTL facility in Almer ´ıa, Spain. The model is a detailed implementation of the Forristal approach [16], it is highly customizable and can be used to model any kind of PTC solar ﬁeld. The paper is organized as follows: section 2 presents the PTC model in detail. Section 3 details the experimental campaign. Section 4 report the results for the steady-state and dynamic validation analysis. Section 5 discusses critical aspects when modelling parabolic through collectors. Finally, section 6 draws the main conclusions of this work. 3 2. Parabolic trough collector modelling The parabolic trough model is developed in the Modelica language [13] and is part of the open-source ThermoCy- cle library [25]. As depicted in Figure 1a, the model relies on a ﬁnite-volume approach for the modelling of the heat collection element (HCE), which is discretized along its axial axis in Nconstant and uniform control volumes (CV). The one-dimensional modelling method is justiﬁed by the large ratio between the diameter and the length of the HCE. Following the object-oriented formalism of Modelica, the PTC model is built by interconnecting two sub-components, 1 2 3 i-1 ii+1 N N-1… … (a) (b) Figure 1: Parabolic trough collector model in ThermoCycle. 1a: One-dimensional ﬁnite-volume modelling of the PTC. 1b: Object diagram of the solar collector model from the GUI of Dymola. i.e. the Flow1D and the SolAbs models. These two are linked together through a thermal port as depicted in Figure 1b. TheFlow1D component simulates the ﬂuid ﬂow in the HCE. In each CV , both mass and energy balances are solved assuming an incompressible ﬂuid and a static momentum balance. Considering the above mentioned assumptions, the ﬁnal conservation law formulations for each CV are reported in Equations 1 to 3, with pressure, p, and speciﬁc enthalpy, h, as dynamic state variables. dM dt=˙msu˙mex=0 withdM dt=V @ @hdh dt+@ @pdp dt! (1) Vdh dt=˙msu(hsuh)˙mex(hexh)+Vdp dt+A˙qconv;f l (2) psu=pex (3) The ”su” (supply) and ”ex” (exhaust) subscripts denote the nodes variable of each CV , Ais the lateral surface through which the heat ﬂux ˙ qconv;f lis transferred to the ﬂuid and Vis the constant volume of each CV . An upwind discretization scheme is selected. @=@ hand@=@ pare treated as thermodynamic properties of the ﬂuid and are directly computed by the open-source CoolProp library, featuring high accuracy Helmholtz energy-based equation of states [4]. The 4 SolAbs submodel simulates the e ective thermal energy transferred from the ambient through the HCE to the ﬂuid. The model is built upon Forristall steady-state equations [15] and implements the dynamic 1D radial energy balance around the HCE, see Figure 2. The model relies on physics-based equations and accounts for: conduction and thermal energy accumulation in the metal pipe; convection and radiation between the glass envelope and the metal pipe; conduction and thermal energy accumulation in the glass envelope; radiation and convection losses to the environment. 𝑞𝑆𝑜𝑙,𝑡 𝑞𝑆𝑜𝑙,𝑔 𝑞𝑟𝑎𝑑,𝑎𝑚𝑏 𝑞𝑐𝑜𝑛𝑣,𝑎𝑚𝑏 𝑞𝑟𝑎𝑑,𝑖𝑛𝑡 𝑞𝑖𝑛𝑡,𝑡 HTF Absorber tube Glass envelope𝑇𝑡 𝑞𝑖𝑛𝑡,𝑔 𝑞𝑒𝑥𝑡,𝑔 Figure 2: Energy balance around the HCE. In blue the glass envelope, in grey the metal pipe and in white the vacuum between the two. Heat transfer is highlighted with red arrows. The environmental parameters, i.e. the direct normal irradiation, DNI, the solar radiation incidence angle, incid, the ambient temperature, T amb, and the wind speed, vwind, are fed to the S olAbs model as inputs. The selected modelling approach allows simulating the relation between the environmental parameters and the axial temperature distribution along the absorber tube. The thermal power transferred to the ﬂuid, ˙ qconv;ﬂ, the thermal losses to the environment, ˙qconv;amb+˙qrad;amb, and the temperatures of both the metal pipe , T t, and the glass envelope, T g, can then be evaluated. Temperatures, heat transfer coe cients and thermodynamic properties are considered uniform around the circumference of the HCE (1-D model). Thermal losses through the support brackets are neglected and solar absorption in the tube and the glass envelope is treated as a linear phenomenon. Unlike Forristall’s original model, the energy balance in the glass envelope and the metal pipe is calculated accounting for their thermal capacity as shown in Equations 4-5. gCp;gdTg dt=˙qint;gDint;g+˙qext;gDext;g (4) tCp;tdTt dt=˙qint;tDint;t+˙qext;tDext;t (5) 5 Temperature dependence of the tube and glass envelopes thermodynamic properties can be activated with two ﬂags, GlassUD andTubeUD . For a detailed description of the modelling approach and heat transfer coe cient calculation, please refer to [15] and [10]. 3. Measurements and experiments 3.1. Experimental facility The experiments were carried out at the Parabolic Trough Test Loop (PTTL), at the Plataforma Solar de Almer ´ıa, Spain. An aerial view of the PTTL system is shown in Figure 3. The solar ﬁeld was characterized by three parallel Figure 3: Aerial view of the PTTL facility at PSA, Almer ´ıa lines of parabolic trough collectors (PTC) from di erent manufacturers AlbiasaTrough, EuroTrough and UrssaTrough. The system was a closed loop, with an East-West orientation and it was charged with the thermal oil Syltherm 800 [11]. The process ﬂow diagram of the PTTL facility is shown in Figure 4. Looking at the bottom of Figure 4 it is possible to recognize the pump which drove the ﬂuid, in liquid state, through one of the three parallel PTC lines of the solar ﬁeld. The ﬂuid was heated from (2) to (3) absorbing the solar energy reﬂected by the collectors to the receiver tubes. At the outlet of the collectors the ﬂuid was cooled down by air-cooler II characterized by a maximum thermal capacity of 400 kW th. Once cooled down the oil reached the pump suction port (1). A 1 m3expansion vessel with Nitrogen, N 2, inertization placed in between the two air coolers was used to regulate the loop pressure, limited to 18 bar. In the whole circuit the oil was maintained in liquid state. Two electric heaters installed at the outlet of the pump allowed controlling the temperature of the oil at the inlet of the PTC lines. A mass ﬂow meter at the outlet of the pump was used to measure the oil mass ﬂow rate. The temperatures at the inlet and at the outlet of the PTC were measured with temperature transmittance (TT) sensors. The direct normal irradiation (DNI) was measured with a pyrheliometer model CH1 by Kipp&Zonen [21]. A weather station installed nearby the solar ﬁeld was used to measure the ambient temperature and the wind speed. A sampling time of 5 seconds was set to acquired the experimental data and LabView was used for data visualization. During the experimental campaign on the PTTL facility, the EuroTrough collectors 6 PT PTPT PTPT PT P T T T PUMP1 AIR COOLERAIR COOLEREXPANSION VESSELURSSATROUGHEUROTROUGHALBIASATROUGH N2 ELECTRICAL HEATERELECTRICAL HEATER2 3Figure 4: Process ﬂow diagram of the PTTL facility with the relative sensors position. (ETC) line was tested. The ETC line was composed by 6 EuroTrough modules connected in series and 18 prototype receiver tubes from a Chinese manufacturer for a total length of 70.8 m and a net aperture area of 409.9 m2. 3.2. Steady-state and dynamic experiments In order to characterize the performance of the ETC line, 24 steady-state points were collected for di erent oper- ating conditions, by varying the pump speed and the temperature at the inlet of the ETC for a total of 5 days of testing. The system was run in stable conditions (TT temperature variations below 2C) for 10 minutes and the steady-state point was recorded by averaging the measurements over a period of 6 minutes. The acquired data were used to cal- ibrate and validate the model in steady-state. In order to characterize the dynamic performance of the ETC, step changes where applied to the pump speed and the ETC inlet temperature. In Table 1, the working conditions of the main variables and of the external ambient parameters during the experimental campaign are reported. The dynamic Table 1: Range of operation of the ETC main variable and of the external ambient condition during the experimental campaign. Variable ˙ moil;su pS F;su Toil;su Toil;ex DNI Tamb vwind Unit [ kg s1] [bar] [C] [C] [ Wm2] [C] [m s1] Min 1.55 12.96 150.05 170.21 593.95 26.23 0 Max 5.03 16.07 304.48 352.28 883.72 33.16 11.23 7 validation was based on three speciﬁc sets of experiments: MFE - Oil mass ﬂow change experiment: a step change was imposed to the oil mass ﬂow rate at the inlet of the ETC by varying the pump speed upwards or downwards starting from a steady-state condition. TE- Oil inlet temperature change experiment: the oil temperature at the inlet of the ETC was varied by shutting down the air cooler starting from a steady-state condition. SBE - Solar beam radiation change experiment: a step change to the solar beam radiations collected on the receiver was imposed downwards and upwards to the parabolic trough collectors by defocusing and focusing the parabolic trough collectors. 4. Simulation results and experimental validation The steady-state and dynamic validation of the ETC dynamic model described in section 2 is presented in this section. The model is compared against experimental data acquired on the PTTL facility at the Plataforma Solar de Almer ´ıa (PSA), Spain. 4.1. Initial conditions, model inputs and parameters In order to compare the experimental data with the modelling results a simulation framework was deﬁned. A schematic of the solar ﬁeld (SF) model is shown in Figure 6. It comprised a mass ﬂow source and a pressure sink connected to the ﬂuid connectors of the SF model. The exogenous inputs (EI) imposed to the ETC model and the relative unit are listed in Table 2. The SF model was parametrized based on the data-sheets of the EuroTrough Table 2: List of exogenous inputs (EI) imposed to the SF model. vwind: wind speed, incid: solar radiation incidence angle, Tamb: ambient tempera- ture, DNI: direct normal irradiation, Fvector : vector for defocusing action, ˙ moil;su: oil mass ﬂow at SF inlet, Toil;su: oil temperature at SF inlet, pex: oil pressure at SF outlet EI v wind incid Tamb DNI Fvector ˙moil;su Toil;su pex Unit [m s1] [Rad] [C] [ Wm2] [-] [kg s1] [C] [bar] collector and the receiver tubes. The incidence angle modiﬁer (IAM), required for the optical e ciency calculation, was computed with an empirical equation as: IAM =1aIincid+aII2 incid cosincid(6) where incidis the incidence angle of solar radiation and aIaIIare two empirical parameters derived through ex- perimental data reported in [27], following the methodology presented in [31]. In order to consider unaccounted optical e ects during testing, e.g., dirt on the parabolic mirrors and tube receivers, the parameter unwas included in the calculation of the optical e ciency. Its value was obtained through a least square optimization routine aimed at 8 Vwind θ Tamb DNI Fvector Tsu ṁsu p h Pressure sink Mass flow source SF SensTp SensTp Figure 5: Modelica model of the ETC line installed at the PTTL facility from the Dymola graphical user interface (GUI). minimizing the error between the simulated SF outlet temperature and the measured one over a six minutes interval of the initial steady-state condition characterizing the ﬁrst day of testing, see Figure 8. In Table 3, the values assigned to the parameters of the SF model are reported. TheGlassUD andTubeUD options of the SF model were set to false during the simulations, i.e. the computation of the density, speciﬁc heat capacity and thermal conductivity of the glass and the metal envelopes was temperature dependent. The heat transfer coe cient was computed based on the Gnielinski single phase correlation [17]. The thermal oil, Syltherm 800, ﬂowing through the tube receivers was modelled as an incompressible ﬂuid using the TableBased framework of the Modelica Standard library. As a consequence no mass accumulation was considered in the receiver tubes. 4.2. Results: Steady-state validation The SF model was compared against 24 steady-state experimental points. The data were acquired at di erent ETC inlet temperatures, by varying the pump rotational speed and the thermal input of the heaters and air coolers . In Figure 3, the model predictions for the temperature at the outlet of the ETC line are plotted versus the experimental values. The SF model is able to reproduce the measured data points with a good agreement. The temperature at the outlet of the collectors is characterized by an accuracy within 3C for most of the tested conditions. For an outlet temperature 9 Table 3: Values of the parameters for the SF Modelica model Parameter Units Value General parameters N - Number of discretized cells [-] 20 L - PTC length [m] 70.8 Ap- Parabola aperture [m] 5.76 Optical properties cl- Mirror reﬂectivity [-] 0.9388 gl- Glass transmissivity [-] 0.92 gl- Glass absorptivity [-] 0.02 gl- Glass emissivity [-] 0.86 tu- Tube Absorptivity [-] 0.7919 aI- IAM coe cient I [-] 4.11 e3 aII- IAM coe cient II [-] 5.513 e5 un- Unaccounted [-] 0.9437 Glass envelope geometries Dgl- External glass diameter [m] 0.12 tgl- Glass thickness [m] 0.0025 Receiver tube geometries Dtu- External glass diameter [m] 0.07 ttu- Glass thickness [m] 0.002 Vacuum properties pvacuum - Vacuum pressure [bar] 1.333 e7 - Ratio of speciﬁc heats for the annulus gas [-] 1.39 mol- Molecular diameter for the annulus gas [m] 3.53 e10 kstd- Thermal conductivity at standard pressure and temperature [W m1K1] 0.02551 below 200C, an accuracy within 4C is found. The larger error as the ETC outlet temperature decreases might be related to the optical e ect parameter un, which is computed for an outlet temperature of 250C, see Figure 8. 4.3. Results:Dynamic validation The SF Modelica model was run on Dymola2017. The Di erential Algebraic System Solver (DASSL) [23] was selected as numerical solver, setting the relative tolerance to 104. In order to increase the model robustness and decrease the computational time, the measured variables imposed as exogenous inputs to the SF model, see Table 2, 10 150 200 250 300 350 Tex,ETC,exp[◦C]150200250300350Tex,ETC,model[◦C] Tex,ETC[◦C] X=Y ±3KFigure 6: Parity plot for the ETC model outlet temperature compared against the experimental steady-state data. are approximated by a spline function in the Modelica /Dymola simulation environment. In Figure 7, the simulated ETC outlet temperature is plotted versus time and compared against the measured data for each of the three performed dynamic experiments. On the left abscissa the measured ETC inlet and outlet tempera- tures and the simulated ETC outlet temperature are plotted versus time. On the right abscissa the DNI and oil mass ﬂow rate, ˙ mwf, normalized with respect to the maximum value reached during the day are reported. For all the plots it is possible to see how the DNI was characterized by variation smaller than 2%. In Figure 7a the results for the MFE experiments and simulation results are reported. Starting from a steady-state condition two consecutive steps of the same magnitude upwards and downwards were imposed to the pump rotational speed at t =450 seconds and t =1430 seconds respectively. As the pump rotational speed was raised at t =450 seconds, the velocity and pressure of the ﬂuid in the high pressure line increased. This resulted in an oil mass ﬂow rate, ˙ mwf, increment of about 40% in around 60 seconds. The increase in oil mass ﬂow rate caused a drop in the temperature at the outlet of the ETC, Tex. The Texdrop was registered at around t =500 seconds, 50 seconds after the oil mass ﬂow rate started changing. This was due to the time required by the oil mass ﬂow rate to reach the outlet of the 70.8 m long receiver tubes. During the experiments the ETC inlet temperature, Tsu, was maintained constant by manually manipulating the air cooler and electrical heaters power. When the oil mass ﬂow rate was changed upwards, as Tsu 11 was expected to decrease the air cooler power was decreased and the electrical heaters power was increased manually, causing a small bump of 2 K in the temperature as it is shown in Figure 7a. The same phenomena in the opposite direction took place when the pump speed was decreased. The ETC outlet temperature presented a symmetrical trend for the upwards and downwards oil mass ﬂow rate change. The SF model was able to well predict the experimental trend both for the upward and downward steps and was characterized by a time constant slightly smaller than the real system. In Figure 7b the TE experiments and simulation results are reported. Starting from a steady-state condition the air-cooler was turned o at t=900 seconds. This resulted in an increase of Tsuand a consequently growth of Tex delayed by around 100 seconds due to the time required by the oil mass ﬂow to travel through the tube receiver. The shut-down of the oil-cooler did not allow to impose a step to Tsuwhich increased with a slow ﬁrst order trend. The large time constant characterizing Tsudeﬁned the change of the outlet ETC temperature. The SF model was able to correctly predict the experimental results including the delay characterizing the Texchange. Finally, in Figure 7c, the SBE experiments and simulation results are shown. Starting from a steady-state condi- tion the ETCs were defocused at t =360 seconds, such that no solar radiation was reﬂected to the receiver tubes. This caused a sudden decrease of Texwhich reached the Tsuvalue in about 200 seconds. The ETCs were focused again at t=650 bringing Texback to its initial value. During the experiment the oil mass ﬂow rate and Tsuwere kept constant. The latter was maintained at its initial value by manually manipulating the power of the two electrical heaters installed after the pump. This resulted in a small bump of less then 4 K after the collectors were focused at t =700 seconds. TheTexwas characterized by a symmetrical behaviour during the focusing-defocusing experiments, as the thermal energy losses were relatively small. The SF model was able to replicate the trend and presented a slightly smaller time constant than the real system. Overall it can be concluded that the SF Modelica model was capable of predicting the physical phenomena character- izing the real system behaviour during the three performed experiments and can be considered validated. In Figures 8 - 9 the simulation and experimental results for all of the six days of the experimental campaign are reported. In Figure 8 - Day I , the three minutes time over which the unparameter was optimized are highlighted by two vertical black dotted lines. During Day 6, continuous changes were imposed to the PTTL facility to test the model during highly variable conditions. As shown in Figure 9 - Day VI , the model is able to correctly predict the collector outlet temperature despite the extreme variations. 12 0 500 1000 1500 2000280300320340360380400Temperature [◦C]Day:IVa) MFE: Oil mass ﬂow change Tsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 500 1000 1500 2000200220240260280300320Temperature [◦C]Day:Vb) TE: Oil inlet temperature change Tsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 500 1000 1500 2000 Time[sec]180200220240260280300Temperature [◦C]Day:Ic) SBE: solar beam change Tsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-]Figure 7: Simulation and experimental results plotted versus time for: a) MFE - Mass ﬂow change experiment b) TE - inlet ETC temperature change experiment c) SBE - solar beam radiation change experiment. The measured inlet and outlet ETC temperatures and the outlet SF model temperature are plotted on the left abscissa. The normalized DNI and oil mass ﬂow rate values are plotted on the right abscissa. 13 0 2000 4000 6000 8000 10000180200220240260280300Temperature [◦C]Day:ITsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 2000 4000 6000 8000 10000 12000150200250300350400Temperature [◦C]Day:IITsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 2000 4000 6000 8000 10000 12000 14000140160180200220240260280300Temperature [◦C]Day:IIITsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-]Figure 8: Simulation versus experimental results for the ﬁrst three days of the experimental campaign plotted versus time. 14 0 2000 4000 6000 8000 10000 12000280300320340360380400Temperature [◦C]Day:IVTsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 2000 4000 6000 8000 10000 12000 Time[sec]200220240260280300320Temperature [◦C]Day:VTsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-] 0 1000 2000 3000 4000 5000 6000 7000 8000150200250300350Temperature [◦C]Day:VITsuexp Texexp Texsim DNI ˙mwf 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-]Figure 9: Simulation versus experimental results for the second three days of the experimental campaign plotted versus time. 15 4.4. Simulation tool A simulation application of the developed PTC model was built as a tool to reproduce the results presented in section 4. This application can be also useful for studying the system dynamics and to evaluate the inﬂuence of the model parameters. This simulator is open source and is freely available at https://ciemat-psa.gitlab.io/ surf-simulator/projects/EuroTrough . Currently, there are binary versions for Linux and Windows platforms. Figure 10 shows some screenshots of the application. The application includes the Modelica model exported following the Functional Mock-up Interface (FMI) standard, input ﬁles, experimental results, diagrams and documen- tation about the model and experiments. (a) PTC experimental and simulated outlet temperatures (b) Summary table (c) Fluid, tube and glass temperatures in each CV Ambient temperature = 29.896 ºC 270.297 ºC 1.995 kg/sDirect Normal Irradiance = 871.601 W/m2 335.759 ºCFocus = 1Wind speed = 13.054 km/h 335.944 ºC Simulatedoutlet temperatureExperimental outlet temperatureInlet temperature Inlet mass ﬂow rateAngle of incidence = 18.848 º (d) Diagram Figure 10: EuroTrough simulation tool. In the main window menu, one of the six operating days, previously discussed in section 4.3 ( Day I -IV), can be selected. Model parameters (see Table 3) are shown in a tree structure on the top left side, where the user can change their default values. Simulation controls are shown on the bottom left side. When the simulation is ﬁnished, a particular time instant can be selected by manipulating the simulation bar. Inputs and simulation results are shown on 16 the right top side. Several tabs organize this information. A summary in a table displays some variables’ values for a particular point in time (see Figure 10b). Simulation results are also compared against experimental data in line plots (see Figure 10a). A bar plot presents the ﬂuid, tube and glass temperatures for a particular point in time in each CV (see Figure 10c). On the bottom right side, there three tabs, the authors tab provides information about the authors, the resources tab can include documents, pictures and external links and the model &experiment tab provides additional information. There is a thumbnail in this tab. A diagram of the process is displayed in another window when the thumbnail is clicked. This diagram can graphically describe the process and displays information about a particular point in time of the simulation (see Figure 10d). Plots have contextual menus which allow the user to change their appearance and conﬁguration. Additionally, results in plots can be exported as data or graphs to ﬁles or the clipboard. 5. Discussion This work aims at proposing a tool to analyse the unsteady operations of parabolic through collectors, with a special attention to the following characteristics: Satisfactory accuracy for engineering scopes Low computational time The SF model is based on the ﬁnite volume method, characterized by a trade-o between model accuracy and com- putational time: increasing the number of CVs leads to better accuracy but negatively a ects the computational e ort. In order to investigate the e ect of the level of discretization on the performance of the SF model when compared to the experimental results a parametric analysis was performed. The SF model, discretized with a number of control volumes (CVs) varying from 1 to 50, was simulated to replicate the experimental data of Day IV, see Figure 9. The results are displayed in Figure 11a where the simulated SF outlet temperature for the di erent levels of discretization is plotted versus time and compared against the measured experimental data on the left abscissa. On the right abscissa the nominal DNI and oil mass ﬂow rate are plotted. Overall as the level of discretization increased the SF outlet temperature got closer to the measurements data. From 10 to 50 CVs the improvement in model accuracy was negligible. On the other hand the 5 CVs and 1 CVs SF model presented a slower time constant compared to the real system and were not able to properly predict the di erent undershoot and overshoot characterizing the measured outlet ETC temperature when the boundary conditions where changed, e.g., step change in the mass ﬂow (MFE) or defocusing-focusing (SBE). In Figure 11b the percentage computational e ort (PCE) deﬁned in equation 7 as the ratio of the computational time (Time Comp) with respect to the simulated real time (Time Real), is plotted for each simulation result. All the simulation results were characterized by a much shorter time compared to the real simulated time. This is related to 17 the remarkably simple simulation framework on which the modelling results were based on (see section 4.1). PCE =Time Comp Time Real100 (7) The computational time increased exponentially with the increase of number of CVs with the 1 and 5 CVs SF models being one order of magnitude faster than the higher discretized model. In order to assess the discrepancy between the di erent CVs discretization levels, the total energy absorbed by the thermal oil in the ETC collectors, Ewf, was computed as the integral of the thermal power over the simulated time, around 4 hours, and compared with respect to the 50 CVs model which was taken as a reference. The percentage relative error ¯ for each SF model was computed as: ¯"(k)=100jEwf;50CVsEwf;kj Ewf;50CVsk2[1;5;10;20]: (8) The results are reported in Table 4. As it possible to see, the overall percentage relative error on the total energy Table 4: Total energy percentage relative error for the di erent levels of discretization of the SF model. Model ¯ "[%] SF CVs 1 0.5 SF CVs 5 0.18 SF CVs 10 0.08 SF CVs 20 0.03 absorbed by the ﬂuid over 4 hours of simulation with respect to the 50 CVs SF reference model was negligible for all the tested levels of discretization. 18 0 2000 4000 6000 8000 10000 12000 Time [sec]280300320340360380400Temperature [◦C]Day:IVa) SF CVs parametric analysis 0.00.20.40.60.81.01.21.41.6 DNI - ˙mwf[-]Tsuexp Texexp DNI ˙mwf Texsim CVs:2 Texsim CVs:5 Texsim CVs:10 Texsim CVs:20 Texsim CVs:50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 PCE [ %]25102050#of CVs in SF FV modelsb) Computational effort by discretized volumes Figure 11: Simulation results versus the experimental results for each full day of the experimental campaign. PCE: percentage computational e ort. 19 6. Conclusions This paper presents a dynamic model included in the ThermoCycle modelica library for the modelling of parabolic through collectors. The proposed model is validated against experimental data acquired on the PTTL facility at the Plataforma Solar de Almer ´ıa (PSA), Spain. Steady-state and dynamic experimental data were obtained at di erent op- erating conditions by varying the pump rotational speed, the heater and cooler set-points and by focusing-defocusing the collectors. A ﬁrst validation is performed against 24 steady-state data points. A second dynamic validation is carried out with 3 sets of experiments by varying the oil mass ﬂow rate (MFE), the oil inlet temperature (TE) and the solar beam radiation (SBE). The main outcomes of this study are reported hereunder. The steady-state validation shows a good agreement between experimental and simulated temperature at the outlet of the collectors. Most of the data are reproduced with an accuracy below 3C. For temperature below 200C, the temperature is predicted with a 4C error. The simulation results obtained for the oil mass ﬂow (MFE), the oil inlet temperature (TE) and the solar beam radiation (SBE) experiments showed a good overlap with the experimental results. The developed solar ﬁeld model structure proves to be e ective to predict the dynamic of a real line of solar collectors. A minimum discretization level of 20 CVs was found to be a good compromise between model accuracy and simulation speed if the ETC outlet temperature had to be precisely predicted, e.g., the SF model is used as a reference to develop and test model based control strategies. In light of the obtained results a lumped SF model is recommended if the performance of the ETC collectors are analysed on a daily or longer time frame. This approach allows to signiﬁcantly decrease the computational time while maintaining a satisfying level of accuracy. It was proven that the modelling approaches adopted led to satisfactory results for the simulation of parabolic trough collector systems. The proposed solar collector model together with the test cases is released as open-source and is available in the latest version of the ThermoCycle library. It should be noted that the model is not suitable for the simulation of start-up or shut-down of the collectors, as the proposed ﬁnite volume approach does not handle zero ﬂow conditions. 7. Acknowledgements The results presented in this paper have been obtained within the frame of the SFERA II project. These ﬁnancial supports are gratefully acknowledged. Furthermore, the authors want to thank the ﬁnancial support received from the BRICKER project (www.bricker-project.com). This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement No 609071. 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