A new concept of solar thermal power plants with large-aperture parabolic-trough collectors and sCO2 as working fluid

Energy Conversion and Management 199 (2019) 112030

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A new concept of solar thermal power plants with large-aperture parabolictrough collectors and sCO2 as working fluid

T

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Mario Biencintoa, , Lourdes Gonzáleza, Loreto Valenzuelab, Eduardo Zarzab a b

CIEMAT, Plataforma Solar de Almería (CIEMAT-PSA), Av. Complutense 40, 28040 Madrid, Spain CIEMAT, Plataforma Solar de Almería (CIEMAT-PSA), Ctra. Senés, km 4.5, 04200 Tabernas, Almería, Spain

A R T I C LE I N FO

A B S T R A C T

Keywords: Parabolic-trough collector Solar thermal power plant Pressurized gas Supercritical carbon dioxide Molten salt Simulation model

The use of pressurized gases as working fluid in parabolic troughs has been proposed in recent works to avoid environmental issues and reduce electricity costs in solar thermal power plants. However, such technology still poses great uncertainties regarding its efficiency and feasibility. To overcome the limitations of pressurized gases, this study proposes a new concept of solar thermal power plant with large-aperture parabolic-trough collectors using CO2 in supercritical state (sCO2) as working fluid and molten nitrate salts as thermal storage medium. A modular design for the solar field, reducing the number of blowers and heat exchangers and minimizing the molten salts hydraulic circuit, is also described. To assess the performance of the new concept, its expected annual efficiency is compared to the efficiency of a reference solar thermal power plant using thermal oil as heat carrier in the solar field. To that purpose, two simulation models are developed in the TRNSYS software environment to reproduce the behaviour of both the new solar power plant with sCO2 and the reference plant. In addition, a parametric study is carried out by means of the simulation model to optimize net annual production as function of outlet temperature and collection area of the solar field. Besides, a preliminary economic assessment is performed to predict expected costs of electricity generated with the new concept of plant. The results of this work suggest that the new concept of solar plants proposed can achieve higher annual efficiencies (about 0.5% increase) and lower electricity costs (around 6% savings) than conventional solar thermal power plants with thermal oil.

1. Introduction Solar Thermal Power Plants (STPPs) based on Parabolic-Trough (PT) collectors are nowadays a successful technology with about 5000 MWe installed and in operation around the world [1]. Most of them operate with synthetic oil as heat transfer medium in receiver tubes installed in the solar field, but recently other working fluids, such as water or pressurized gases, are being investigated in order to improve the performance of PT technology and avoid the environmental issues of synthetic oils [2]. The use of pressurized gases as working fluid in PT collectors [3,4], and specifically CO2 [5,6], has been proposed and analysed in previous works. Moreover, a test facility including a PT collectors’ loop with gas as working fluid has been successfully erected and operated at the Plataforma Solar de Almería, showing promising results [7]. Besides, CO2 behaves as a supercritical fluid at temperatures and pressures above its critical point (30.98 °C, 73.77 bar). Due to its increased

density and conductivity compared to its gaseous state, CO2 in supercritical conditions (sCO2) provides further advantages for thermal-hydraulic systems in terms of heat transfer and required pumping consumptions. In this way, sCO2 has been suggested to be used as coolant in nuclear reactors [8] and to drive innovative thermodynamic cycles [9], both Rankine [10] and Brayton-based [11] cycles. Additionally, the integration of such advanced power cycles with solar thermal technologies has been investigated [12,13]. Such features have boosted the interest of sCO2 to be used as HTF in tubular receivers of STPPs [14], either for parabolic troughs [15] or central receiver systems [16,17]. To this purpose, models to simulate the behaviour of sCO2 have been developed; for instance, a simplified 1D model is described and validated in [18]. The main advantage of both pressurized gases and sCO2 lies in the possibility of increasing fluid temperature at the outlet of the solar field, thus involving a higher performance of the power block and a higher efficiency of the thermal storage, per unit volume, with molten salts.

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Corresponding author. E-mail addresses: [email protected] (M. Biencinto), [email protected] (L. González), [email protected] (L. Valenzuela), [email protected] (E. Zarza). https://doi.org/10.1016/j.enconman.2019.112030 Received 11 July 2019; Received in revised form 4 September 2019; Accepted 5 September 2019 Available online 13 September 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature Ac F Gb K K(θ) L m ṁ Nsubfields P Q̇ T W Ẇ

sCO2 SF SG STPP TES

net collection area, m2 proportionality factor, – direct normal solar irradiance, W/m2 economic cost, € incidence angle modifier, – length, m mass, kg mass flow rate, kg/s number of subfields, – pressure, bar thermal power, W temperature, °C electric energy, kWh electric power, W

Greek symbols Δ η θ

increment or variation efficiency or performance factor, – incidence angle, °

Subscripts abs amb clean dump fluid fuel gross invest loss net opt,0° out ref salts sh u

Acronyms CRF DNI HTF HX IAM LCoE LMTD NTU O&M PSA PT PB RMSE

supercritical CO2 solar field steam generator solar thermal power plant thermal energy storage

capital recovery factor, – direct normal solar irradiance (equivalent to Gb), W/m2 heat transfer fluid heat exchanger incidence angle modifier, – levelized cost of electricity, €/MWh log mean temperature difference number of transfer units operation and maintenance Plataforma Solar de Almería parabolic trough power block root mean squared error

absorber tube ambient cleanliness energy dumping working fluid fossil fuel used gross electric power investment thermal or electric losses net electric power peak optical outlet reference value molten salts shadowing useful

configuration is proposed in this study to take advantage of the new concept and two simulation models are developed to predict the behaviour of these plants with enough accuracy and flexibility. In addition, a parametric study is performed in this work to find out the optimal design temperature at the outlet of the solar field. To this purpose, a STPP with PT collectors in the solar field is simulated using CO2 as heat transfer fluid (HTF), with 100 bar working pressure and design outlet temperature ranging from 473 to 523 °C. Such conditions correspond to a supercritical fluid. To reduce pressure losses, receiver tubes with larger outer diameter (around 89 mm, commercially available [23]) than standard tubes (70 mm) will be used. Besides, IberTrough-type PT collectors of 100 m length will be considered for the solar field, with 7.334 m aperture width instead of 5.76 m as used in most of the existing commercial STPPs with PTs. Molten salts will be employed as secondary transfer fluid and thermal storage medium. The advantages of such improvements will be estimated by comparing the annual electricity production of the new STPP to the output of a reference plant using thermal oil and state-of-the-art PT collectors. Both plants will include a power block with 55 MWe gross electric power, equivalent to the gross output of most commercial STPPs in Spain. The plant configuration with thermal oil is included as a reference to compare the new technology with commercial STPPs, which are supposed to be optimized, in terms of annual efficiency and preliminary economic estimations. The evaluation of specific advantages and cost savings of large-aperture PT collectors with thermal oil has been addressed in other studies [22,24] and is out of the scope of this work. This article is structured as follows: Section 2 describes the new concept of STPP and the reference plant; Section 3 explains the model of the solar plants to be simulated, either with sCO2 or thermal oil; a brief validation of such models using experimental data from a test facility with CO2 and from a commercial STPP with thermal oil is

Nonetheless, pressurized gases also present some drawbacks when used in PT collectors [19], such as higher thermal losses in the solar field due to higher temperatures, what implies a lower solar field performance, the necessity of higher pipe thicknesses to work at high pressures, great power consumptions in gas pumping due to pressure losses, etc. There are additional uncertainties related to molten salt circuits (heat tracing, cold points, etc.) and the specific components required (gas blowers and gas/salt heat exchangers) when considering STPPs using sCO2 in the solar collectors and a molten salt thermal storage system. Up to date, studies carried out for STPPs with pressurized gas and standard PT collectors (EuroTrough-100 m, absorber steel tube with 70 mm outer diameter) have resulted in annual electricity yields that may become similar [20] to the production of commercial STPPs using thermal oil as heat transfer medium in the solar field. Besides, the proposed modular design required a great number of blowers and gas/ salt heat exchangers to limit pressure losses and involves high piping lengths in the molten salts circuit. The high cost and difficulties concerning operation and maintenance of such components, together with the expected problems (freezing, cold points, feasibility of components, etc.) for large piping systems with molten salts [21] cast doubts on the technical and economic viability of PT technology with pressurized gases. The recent development and commercialization of PT collectors with larger aperture width [22] than conventional PTs enables the use of receiver tubes with larger diameters. A larger diameter of receiver tubes implies lower pressure losses, which in case of pressurized gases as working fluid would allow the reduction of the number of blowers and gas/salt heat exchangers and the minimization of the molten salts circuit. Nevertheless, the use of receiver tubes with larger outer surface involves an increase in thermal losses, thus leading to a lower efficiency of the solar field. In order to analyse such uncertainties, a specific plant 2

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gas/salt HXs are isolated at the gas side. At sunrise, CO2 will be circulated through the solar collectors, heating up the gas subfields until an equilibrium temperature of about 290 °C is reached. At that moment the gas and salt circuits will be connected by means of the heat exchangers to transfer the useful heat obtained in the solar collectors to the molten salts. Molten salts from the SF will be led either to the hot storage tank when their temperature is beyond a specific minimum value (about 430 °C) or to the cold storage tank otherwise. The salts will be circulated from the hot tank to the steam generation train to preheat, evaporate and superheat the water required by the steam power block. The minimum temperature value for the molten salts must guarantee that neither freezing nor cold points occur throughout the entire steam generation train. Therefore, such minimum value will be determined by the salt temperature at the outlet of the SG. In order to avoid dangerous conditions, high loads will be preferred for the SG, resulting in outlet flows of molten salts from the hot storage tank that will be always close to their nominal value. To minimize the start-up time of the SF, the initial daily warm-up of CO2 in the HX and piping of each subfield can be performed with the help of a system of valves such as the one shown in Fig. 3. In this way, opening valves 1 and 2 (see Fig. 3), keeping the rest closed, allows fluid circulation only through the solar collectors’ loops without going through the HX. This configuration enables the gas circuit warm-up avoiding thermal shocks in the HX due to temperature differences between gas and molten salts. On the other hand, with valves 4 and 5 opened (and the rest closed) CO2 is recirculated only through the HX, enabling the prior heating of this component by means of the molten salts. Finally, when CO2 circuit temperatures are high enough, the normal operation of the subfield can be performed by opening valves 2, 3 and 4 and closing valves 1 and 5, circulating the gas through both the solar collectors’ loops and the HX. In order to observe the behaviour of CO2 within the boundaries of supercritical conditions, a temperature-entropy (T-s) diagram is depicted in Fig. 4, including the proposed ranges for nominal operation of sCO2 and possible regions in which fluid conditions may be enclosed during non-nominal operation (for instance, shutdown or start-up). Blue lines in Fig. 4 (solid for the maximum range, dashed for the minimum range specified in Table 1) show the nominal operating conditions established for the collectors’ loop, which correspond to a supercritical fluid since they are above the supercritical limit curve (in dashed orange line). During shutdown and start-up processes of the subfields, pressure and temperature are commonly lower than nominal values and therefore CO2 falls below the supercritical limit, becoming either a gas or a liquid (or even saturated fluid when it is below the saturation line) according to its corresponding temperature and entropy (which in turn depends on the fluid pressure). Although fluid circulation with liquid CO2 may cause damage to blowers, those conditions

included in Section 4; Section 5 summarizes the comparison of results between both plants, along with a parametric analysis of the optimal working temperature for the new STPP; finally, overall conclusions are presented in Section 6. 2. Description of the solar plants The solar field of the reference STPP is composed of 156 loops with 6 units per loop of EuroTrough PT collectors 100 m long each that uses thermal oil as HTF in the receiver tubes, similar to commercial STPPs in Spain. The plant includes a two-tank thermal energy storage (TES) system with 1 GWh of storage capacity (around 7.5 h of generation capacity at nominal conditions) and molten salts as heat storage medium. The power block consists of a reheat steam Rankine cycle with 6 turbine steam extractions, considering a wet cooling system. On the other hand, the solar field (SF) in the new CO2 plant is composed of 23 subfields (the number of subfields is modified during the optimization process performed in this study). Each subfield includes 16 loops sharing the same blower and gas/salt heat exchanger with 2 IberTrough-type collectors per loop, as shown in Fig. 1. IberTrough-type PT collectors are 100 m long and have a parabola aperture length of 7.334 m and a focal length of 2.172 m, and have been installed and tested as a prototype at the PROMETEO test facility of the Plataforma Solar de Almería [25]. For this study, the solar collectors are equipped with receiver tubes designed for high pressure and temperature conditions with an outer diameter of 88.9 mm, instead of conventional 70 mm, to reduce fluid pressure losses. Such value has been selected considering commercially available versions of receiver tubes for large-size PT collectors [23]. The useful heat absorbed by CO2 in solar collectors will be transferred by means of the gas/salt heat exchanger in each subfield to a molten salts circuit, which will connect the SF to the two-tank TES system. The power block (PB) and the steam generator (SG) considered for the new plant will be the same as those in the reference STPP, although the specific fluid characteristics concerning inlet temperature and freezing point must be taken into account. A general diagram of the solar field with the distribution pipes of the molten salts circuit and the central power island, including the PB and storage tanks, is shown in Fig. 2. The main features and parameters of the two plants are summarized in Table 1. The distance between adjacent collectors’ rows corresponds roughly to three times the collector’s aperture width, whereas the dimensions of solar collectors and receiver tubes are taken from manufacturer’s data [23]. The net collection area initially selected for the SF in the sCO2 plant is approximately equal to that of the reference plant. Nevertheless, the SF size is modified in further steps of this work to optimize its design. This variation involves changes in both the number of subfields composing the SF and the size of the TES system. Besides, a range from 473 to 523 °C is considered for the outlet temperature of the solar collectors in order to assess an optimized value according to certain criteria. The values shown in Table 1 for the size of the TES system and the nominal gross efficiency of the PB in the plant with CO2, obtained with the expressions and analytical methods described in Section 3, are given within a range whose margins are related to the nominal temperatures considered at the outlet of the collectors’ loops. Since PB efficiency is expected to increase with temperature, the lowest temperature (473 °C) is associated to the minimum value of PB efficiency (41.3%). On the other hand, since storage energy density per unit mass raises with higher thermal differences, the required storage size will be inversely proportional to the temperature difference between outlet and inlet. In this way, the minimum temperature (473 °C) corresponds to the largest amount of storage medium (20000 t). Regarding the operation of the new plant, molten salts in the solar field are expected to be recirculated through the cold storage tank during the night, while CO2 circulation is stopped in the subfields and

Fig. 1. Diagram of each subfield for the solar power plant using CO2 as HTF, including solar collectors, heat exchanger and blower. 3

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Fig. 2. Diagram of the solar field for the STPP using sCO2 as HTF, including subfields with gas (marked with dashed orange rectangles), distribution pipes with molten salts (hot salt pipes in continuous red colour and cold salt pipes in continuous blue colour) and a central power island.

establishing its required mass flow rate and calculating thermal and hydraulic balances in the solar field for dynamic flow conditions. Otherwise, there is no fluid circulation in the solar field and energy balances are calculated accordingly (i.e., for static flow conditions). The operation of the TES system and the power block is specified in the following blocks of Fig. 5. If the mass flow rate and outlet temperature in the solar field is equal to or higher than the reference mass flow and minimum temperature required for the HTF to run the power block, the PB is operated and the remaining mass flow is sent to charge the TES system. In case that the TES is full, it cannot be further charged, causing a partial defocusing of the solar field in the subsequent time step. As a result, the corresponding thermal energy that cannot be used is accounted as “dumped energy”. When fluid conditions are not sufficient to operate the power block and there is enough storage load, the TES system is discharged to complete the SF support and hence the power block operates in storage mode. PB operation involves the calculation of balances in the steam generator and the power block itself, along with the evaluation of parasitic consumptions, which enables obtaining net electric power from gross electric power. Parasitic losses are also calculated when the PB is stopped. The main results of the simulation (gross and net electric power, outlet and inlet temperatures at significant points of the system, mass flow rates, storage level, etc.) are recorded in an output file each time step. When the last time step is attained, the simulation ends. Otherwise, some relevant variables of the model are stored to summarize the system state and the simulation continues by reading weather data for the next time step. The general layout of the TRNSYS model for the conventional solar

would appear only in cold nights of winter, when the fluid is stopped. In any case, the experience at the PSA has shown [26] that the running of blowers at minimum speed may provide the fluid with enough heat to evaporate the remaining liquid, thus enabling a safe operation. The geographical coordinates of the foreseen location of the SF for both plants are 37°05′27.8″ N and 2°21′19″ W, corresponding to Plataforma Solar de Almería [27] (Spain). 3. Simulation model The simulation model for both plants has been implemented within the TRNSYS software environment [28]. The model for the reference STPP using thermal oil as HTF is based on the one considered in previous works [29,30,20]. Nevertheless, it incorporates several improvements and additional components to simulate in a more accurate and flexible way some elements that will be used in both plants, such as the power block, steam generation train and heat exchangers. The basic algorithm for the calculations performed in the simulation models, which can be applied to both the reference STPP with thermal oil and the new one with sCO2, is summarized in the simplified flow chart displayed in Fig. 5. As seen in Fig. 5, weather data are read from the input file to perform the corresponding calculation of solar angles (zenith angle, incidence angle on solar collectors, tracking angle). The available amount of solar radiation (DNI), together with the previous state of the system, determines the operation mode of the solar field (startup, shutdown, regular operation, etc.). When the DNI is above a minimum value (namely, 100 W/m2), the HTF is circulated through the solar field, 4

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specifically developed to retain values from the previous time step (type293) or to obtain thermo-physical properties of working fluids (type220). Also, in Fig. 6 some macro-components such as the solar collectors’ loop (‘Collectors Loop’) and the thermal energy storage system (‘Storage System’) have been extended to show in detail the components of the most relevant subsystems of the plant. In a similar way, Fig. 7 shows the TRNSYS model for the new solar plant with sCO2, also including extended diagrams for the subsystems corresponding to the gas subfield (‘Collectors Subfield’) and the thermal energy storage system (‘Storage System’). Both the solar collector loops in the reference plant model and the subfields in the new solar power plant are basically built upon the model of solar collector (type203), which enables the selection of the type of solar collector, parameters and working fluid, and the model of pipe (type202) with thermal insulation. In general terms, the thermal model of PT collectors is performed by evaluating the useful power gained by the fluid, Qu̇ , with an energy balance between solar power absorbed by the system and thermal losses ̇ . If the effect of kinetic energy due to the to the environment, Qloss variation in fluid velocity is neglected, the useful power can be obtained with the following expression:

Table 1 Main features and parameters considered for each type of STPP. Parameter/Type of plant

Reference

New concept

Working fluid in receiver tubes Type of solar collector Aperture width (m) Focal length (m) Net collection area for each collector (m2) Total length of receiver tube for each collector (m) Outer diameter of the metal receiver tube (m) Inner diameter of the metal receiver tube (m) Peak optical efficiency (%) Cleanliness factor of the mirrors (%) Distance between collector rows (m) Number of collectors per loop/subfield Number of loops/subfields in the solar field Net collection area of the solar field (m2) Nominal temperature at collectors’ loop outlet (°C) Nominal temperature at collectors’ loop inlet (°C) Nominal pressure at collectors’ loop inlet (Pa) Fluid in the thermal storage system Size of the thermal storage system (t) Efficiency of HXs and steam generator (%) Nominal gross efficiency of the power block (%) Nominal gross electric power (MWe)

Therminol® VP-1 EuroTrough 5.76 1.71 548.35 98.7

sCO2 IberTrough 7.334 2.172 698.2 98.7

0.07

0.0889

0.065

0.074

75.5 97 16.5 6 156 513255.6 393

75.5 97 25 2 / 32 368 / 23 513875.2 473…523

298

310

2.7·10

6

107

Solar Salt 25500 99 39.5

Solar Salt 15555…20000 99 41.3…42.5

55

55

̇ Qu̇ = ηopt ,0° ηclean ηsh K (θ ) Gbcos (θ ) A c − Qloss

(1)

In Eq. (1), Gb is the direct normal irradiance, Ac the net collector aperture area, θ the incidence angle, K(θ) the incidence angle modifier, ηopt,0° the peak optical efficiency, ηclean the cleanliness factor and ηsh the shadowing factor between adjacent collector rows. The incidence angle modifier (IAM) for EuroTrough-type collectors was inferred from the experimental characterization of EuroTrough-II concentrator at the PSA by Geyer et al. [31]. On the other hand, the correlation applied for the IAM of IberTrough-type collectors using 88.9 mm outer diameter tubes (Eq. (2)) was obtained from optical simulations with a ray-tracing tool [32] applying a similar procedure to the one presented by Sallaberry et al. [33]:

K (θ) = 1 − (7.072∙10−4∙θ + 1.582∙10−5∙θ 2 − 1.169∙10−7∙θ3)/cosθ

(2)

The comparison between IAMs for both solar collectors for different values of incidence angle is represented graphically in Fig. 8. According to this figure, a better optical behaviour (IAM closer to 1) is expected in IberTrough-type collectors for high values of the incidence angle. Standard receiver tubes SCHOTT PTR®70 from the first generation have been considered for EuroTrough-II concentrators, whose thermal losses have been experimentally evaluated from outdoor tests at the PSA [34]. The resulting expression, in W, is given as function of ΔTfluidamb, the difference between the average temperature of the fluid and ambient temperature, in °C, and Labs, the length of the absorber pipe section to be considered, in m: 4 ̇ = (0.342∙ΔTfluid − amb + 1.163∙10−8∙ΔT fluid Qloss − amb ) ∙Labs

(3)

Expression (3) is extrapolated for IberTrough-type collectors taking into account that a larger outlet surface of the receiver tube, which is directly proportional to its diameter, involves thermal losses that are proportionally higher [35]. In this way, Eq. (3) is applied but multiplying by the diameter of the new tubes (88.9 mm) and dividing by the diameter of standard tubes (70 mm). In this case the temperature difference ΔTfluid-amb between fluid and ambient is obtained by calculating the heat transfer coefficients between receiver tube and fluid with the Dittus-Boelter correlation [36] for thermal oil and for CO2. Then, the corresponding temperature differences are subtracted and added, respectively, to obtain the resulting ΔTfluid-amb to be applied in Eq. (3). This assumption is supported by experimental tests performed at the PSA [26], yielding similar efficiencies for CO2 to those expected for thermal oil for the same temperatures. The component for connecting pipes (type202) is based on a model of thermal nodes composed of metal tube and thermal insulation (see

Fig. 3. Schematic diagram of the system of valves for the operation of gas/salt HX and blower of each subfield in the STPP using sCO2 as HTF.

plant with thermal oil is depicted in Fig. 6, including equation editors, components from the standard TRNSYS library to read input data (Type9a) or determine solar angles (Type16g) and components 5

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Fig. 4. Temperature-entropy diagram of the CO2 in each collectors’ loop for the STPP using sCO2 as HTF, including the selected range for nominal operation.

efficiency of the new concept. In this way, Eq. (4) also fits for the reference plant but using 2.4·109 as numerator in the first term and Nsubfields = 23. The heat exchangers that transfer the useful energy from the solar field to the TES system both in the reference plant (oil/salts) and in the new plant (sCO2/salts) are modelled (type206) by using the Number of Transfer Units (NTU) method [36]. On the other hand, the model to simulate the performance of the steam generation train is implemented with a new component (type255) that applies the Log Mean Temperature Difference (LMTD) method [36] to each of its elements: preheater, evaporator, superheater and reheater. Such TRNSYS components provide the required flexibility in each plant model by enabling the selection of parameters such as the working fluid. The model of the PB is implemented in a new component (type250), described in [38,39], that analyzes the system behaviour in both nominal and part-load conditions using the Spencer-Cotton-Cannon method [40]. Besides, each plant model estimates electric losses by adding to the pumping consumptions a fixed value, which is different for online and offline conditions, and a variable value depending on the electric load. Those values are adjusted considering the experience [29] in modelling and simulation of commercial STPPs using thermal oil as heat carrier. The main additional parameters assumed in the simulation model for each type of plant are summarized in Table 2. To assess the feasibility of the new STPP concept using sCO2 and to analyse the expected impact of plant configuration on energy costs, a preliminary economic analysis is performed based on the calculation of the levelized cost of electricity (LCoE), given by:

[30]) whose properties are known. Then, an energy balance is applied to calculate thermal losses to the atmosphere due to convection and to the sky due to radiation. Additionally, a mechanism is incorporated to this model to simulate in an easy way the effect of thermal inertia by means of exponential expressions, as described in previous works [20]. The hydraulic model, explained in [30], for both receiver tubes and connecting pipes is based on the evaluation of pressure drop through straight pipes and accessories using the Darcy-Weisbach equation [37], establishing the friction factor according to the turbulence regime of the fluid. The calculation of pressure losses enables the evaluation of pumping consumptions, which are added to the rest of parasitic consumptions of the plant. The TES system in both plants is implemented by means of a component (type240) that models each molten salt tank as a thermal energy storage tank with variable volume (see [20]). The model of the TES system is completed by including piping, associated operation mechanisms and, in the case of the reference plant, the oil/salt heat exchanger. In the case of the new plant, since the storage energy efficiency per unit volume is higher with increasing temperatures, and considering that different sizes for the SF are expected to be analyzed, the TES capacity is not constant for all cases, but it is established according to the specific configuration to be simulated. In this way, a heuristic correlation is applied to determine the total amount of salts for a given nominal outlet temperature Tout,ref, in °C, and number of subfields Nsubfields:

msalt , TES (kg) =

Nsubfields − 10 3.5·109 · Tout , ref − 298 13

(4)

LCoE =

Eq. (4) was obtained considering that the amount of salts will be inversely proportional to the nominal thermal difference in the energy storage system (Tout,ref–298) and directly proportional to the part of SF devoted to energy storage. In this way, since the nominal thermal power required by the PB approximately corresponds to 10 subfields, the second term in Eq. (4) reflects the quotient between the number of subfields above 10 and the excess of subfields corresponding to the reference size (23 subfields). Besides, the numerator in the first term (3.5·109) was obtained by applying a correction coefficient (about 150%) to the equivalent value of msalt,TES·ΔT for the conventional plant with thermal oil in order to take advantage of the higher storage

CRF∙Kinvest + K O & M + Kfuel Wnet

(5)

In Eq. (5), Kinvest stands for the total investment cost of the STPP, KO for the annual operation and maintenance cost, Kfuel for the annual cost of the fuel used, Wnet for the net annual electricity production and CRF for the capital recovery factor, which in turn depends on the annual insurance rate, the effective interest rate and the depreciation period according to the usual definition given in energy standards [41]. The specific costs and economic parameters used in the calculation of LCoE are specified in Table 3. Those values have been obtained from extrapolation of economic data applied in former studies, both to &M

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Fig. 5. Simplified flow chart of the calculations performed in the simulation models for both the reference STPP using thermal oil as HTF and the new STPP using sCO2.

the new technology is expected to be similar to that of conventional PT plants, applying the same specific O&M cost for both STPPs has been considered as a reasonable assumption.

determine electricity costs of the reference plant [42,43] and to evaluate the expected savings in the SF due to the use of collectors with larger aperture [22] or the increase of investment required by components for the new technology using CO2 [44]. Specific costs of the SF, in €/m2, are referred to net collection area, whereas land specific cost, also in €/m2, is referred to land area. O&M costs in Table 3 are taken from [45], weighting the experience in PT plants with thermal oil. No increases in O&M costs are expected associated to solar fields with large-aperture parabolic troughs or to the use of pressurized gases. Since the level of automation for plants with

4. Models’ validation The validation of the CO2 model is performed by using experimental data of the test facility at the PSA with 1 s time step, the same used in the simulation. This test facility is provided with 100 m of EuroTrough PT collectors using conventional receiver tubes with 70 mm outer 7

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Fig. 6. Screenshot of the TRNSYS model for the reference STPP using thermal oil as HTF, showing details of the model of the solar collectors’ loop and the TES system implemented.

the reference STPP. The validation of the reference plant model is carried out by using real data of a commercial STPP in Spain with thermal oil as HTF in the solar field. This STPP includes a two-tank TES system with molten salts, providing around 1.3 GWh of storage capacity, and a power block based on a conventional steam Rankine cycle with 55 MWe gross electric power. Such plant presents similar features to those considered for the reference STPP in Table 1. Operation data from the STPP include DNI, inlet and outlet temperatures from the solar field, mass flow rate of the HTF, gross and net power generated and level of storage load for a cloudy day of spring, the 24th of March, with significant solar transients in order to check the model performance in non-favourable conditions. The data time step is 1 min, also the same as the step used by the simulation. In this case, the model of the reference STPP simulates the control system and plant operation procedures, as well as the behaviour of each subsystem. As a result, mass flow rates and inlet temperatures are not taken from the experimental data but obtained as outputs from the simulation, and then compared to the actual data to validate the whole plant model. The comparison between real data and simulation results is shown in Fig. 10. The results seen in Fig. 10 reflect the accuracy that can be expected from the model in a typical cloudy day. RMSE values calculated throughout the operation period of the solar field (with DNI and mass flow rate higher than zero) are 18.4 °C for the outlet temperature and 154 kg/s for the mass flow rate (around 12% of the maximum flow). Nevertheless, it should be remarked that the inputs for the mass flow

diameter. Details on the collectors’ loop and instrumentation devices, along with their uncertainty ranges, can be found in [7]. The day selected for the validation is the 27th of October 2010, achieving nominal conditions of 500 °C and 44 bar for the CO2. Even though such values of pressure and temperature do not correspond to supercritical CO2, the behaviour of the fluid is expected to be similar to sCO2, thus suggesting a reasonable basis to prove the performance of the solar field model with pressurized CO2 that may be extrapolated to supercritical conditions. The comparison between real data and simulated results is shown in Fig. 9, including measured values of DNI, outlet and inlet temperature, mass flow rate and pressure loss in the collectors’ loop, together with the corresponding values of outlet temperature and pressure loss obtained from the simulation. As seen in Fig. 9, both temperature and pressure loss results of the model closely follow the real data measured at the experimental loop, even with transients in solar radiation resulting from the defocusing of collectors at around 13 and 13:30 h. Root Mean Squared Error (RMSE) values calculated throughout the operation period, i.e. with mass flow rate higher than zero in the collectors’ loop, are 10.1 °C for the outlet temperature and 0.03 bar for the pressure loss. Such figures suggest that a good performance may be expected for the model to simulate the behaviour of pressurized CO2 as working fluid in parabolic-trough collectors. Since the test facility at the PSA contains neither an energy storage system nor a thermodynamic cycle for power generation, the behaviour of such subsystems in the model with sCO2 relies on the validation of 8

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Fig. 7. Screenshot of the TRNSYS model for the new STPP using sCO2 as HTF, including details of a gas solar collectors’ subfield and the TES system implemented.

between simulation outputs and real data in terms of net electricity production is lower than 2% for this period. Taking into account that the day selected for the validation includes significant solar transients, involving increased challenges for a STPP simulation model, these results can be considered accurate enough for the purposes of the proposed study. 5. Results and discussion A two-part study is performed using the simulation models described in Section 3 and meteorological data of a typical year at the PSA. In the first part of the study the net collection area for the plant with sCO2 is the closest possible to the net collection area of the reference plant using thermal oil as HTF, corresponding to 23 subfields. This assumption enables the comparison of results between both technologies. In the second part, a parametric study is carried out regarding the annual electricity production of the plant with CO2 as function of the nominal temperature at the outlet of solar collectors and the SF size. The plant location considered for both parts of the study is PSA, Spain, and the meteorological data correspond to a typical year with an annual DNI balance of 2071.46 kWh/m2 and 3658 h of sunlight, applying a time step of 5 min for both the simulation and input data. In order to compare the daily operation of both STPPs, considering the first part of the analysis with the same collection area, Fig. 11 represents the results of net electric power, electric losses, thermal energy storage load and DNI obtained with the thermal-oil plant model and the sCO2 plant model (with 23 subfields and 493 °C outlet temperature) for four days of spring with different profiles in terms of solar radiation. As seen in Fig. 11, the daily behaviour of electric production with the new STPP is different from the usual yield profile of a conventional

Fig. 8. Comparison between the incidence angle modifier of EuroTrough collector with receiver tube of 70 mm outer diameter and IberTrough collector with 89 mm tube, both 100 m long.

and inlet temperature in the simulation are obtained from the model itself, not from real operation data, affecting in a significant way the outlet temperature results and thus increasing the resulting RMSE values compared to simulations with common inputs (such as Fig. 9). In the case of the electric output and storage load results shown in the lower graphic of Fig. 10 considering the whole simulation period, the corresponding RMSE are 4.1 and 4.2 MWe for the gross and net electric power, respectively, and 1.55% for the TES load. Besides, the difference 9

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Table 2 Main additional parameters assumed in the simulation model for each STPP. Assumed parameter/Type of plant

Reference STPP

New STPP concept

Minimum/maximum mass flow rate per loop in operation (kg/s) Mass flow rate per loop during startup/antifreeze protection (kg/s) Inner/outer diameter of connecting pipes between collectors with thermal oil or between loops in gas subfields (m) Inner/outer diameter of E-W distribution pipes (m) Inner/outer diameter of N-S distribution pipes (m) Insulation thickness in hot/cold connecting pipes of loops (m) Insulation thickness in distribution pipes (m) Nominal temperature difference in hot/cold side of HXs (°C) Nominal temperature difference in hot side of SG (°C) Nominal pressure drop in HTF/salt side of HXs (Pa) Nominal efficiency of HTF pumps or gas blowers (%) Nominal efficiency of salt pumps (%) Nominal efficiency of water pumps in PB (%) Fixed electric losses online/offline (kWe) Variable electric losses at nominal load (kWe)

2.5/9 3/1.28 0.0627/0.073 0.428/0.457 0.67/0.71 0.12/0.1 0.2 6/5 11 2·105/105 85 76 75 2000/850 600

0.4/5 1.2/0.3 0.194/0.219 0.22/0.25 0.48/0.51 0.2/0.15 0.2 7/7 11 3·104/6·104 60 76 75 2000/850 600

step. The results of gross and net annual electricity production of the new STPP with sCO2 for different outlet temperatures and number of subfields are shown in Figs. 12 and 13, respectively, also including in dashed line the production of the reference STPP with thermal oil, even though it corresponds to an outlet temperature of 393 °C, not covered by the x-axis range. As expected, a higher number of subfields implies higher annual electricity values, both gross and net results. Also, the gross annual production of the new STPP with sCO2 is always higher than the production of the reference plant with thermal oil. As seen in Fig. 12, the gross annual electricity production for a given number of subfields decreases with temperature. Such trend may suggest that the efficiency gain in the PB is not able to balance the increasing thermal losses in the SF for higher temperatures when gross electricity is considered. However, in the case of net annual production shown in Fig. 13 a maximum appears for each curve due to the impact of parasitic losses. As a result, the outlet temperature of solar collectors that provides a maximum net annual yield ranges from 503 to 513 °C depending on the number of subfields. In order to assess the impact of pumping consumption and corresponding parasitic losses on the annual electricity yield, Fig. 14 represents the electric losses factor, obtained as the ratio of annual electric losses to gross electricity production (which is in turn the sum of net electricity production and electric losses). Electric losses include pumping consumptions for both HTF (thermal oil or sCO2) and molten salts, together with the rest of parasitic losses considered in the model. Since larger temperature differences between outlet and inlet involve lower mass flow rates in the solar field for the same useful

thermal-oil plant, reaching lower values of net electric power when the solar radiation is high and showing maximum values at night. Such behaviour is due to the effect of electric losses obtained for high values of DNI, given the high electric consumptions for gas pumping in subfields, and to the fact that the TES system is always discharged at nominal flow rate. On the contrary, the TES discharge in conventional STPPs is performed at lower mass flows and temperatures than the values applied in nominal conditions. In this way, the strategy adopted in the STPP with sCO2 involves higher net electric power during the night. On the other hand, Fig. 11 shows that, in this case, the storage load reaches lower values in the STPP with sCO2 than in the reference plant, despite the mass of molten salts is lower (see Table 1). As mentioned above, such values occur because the higher thermal difference experienced by molten salts in the new plant concept increases the storage efficiency per unit mass, taking a better advantage of a given amount of storage medium. For instance, the last day represented in Fig. 11 shows that the TES system for both plants is completely full at sunset, when solar radiation is going down (hour 3834). In this case, the plant with sCO2, in spite of having a lower amount of molten salts in the hot tank, is capable of producing electricity during more hours than the reference STPP. In the second part of the study, both the net collection area and the outlet temperature of the SF are varied. The variation in collection area is carried out by increasing or decreasing the number of subfields, including sets of 4 subfields arranged in additional rows in the diagram of Fig. 2 in order to guarantee a reasonable symmetry in the SF. In this way, the number of subfields will range from 24 to 40 in steps of 4, involving about 90000 m2 of increase in the net collection area for each

Table 3 Specific costs and economic parameters considered in the calculation of LCoE for the two STPPs considered. Element/Type of plant 2

Specific cost SF: solar collectors’ mirrors, structures, tracking systems, foundations (€/m ) Specific cost SF: solar receivers (€/m2) Specific cost SF: piping, insulation, connections (€/m2) Specific cost SF: HTF system, boiler, ancillaries (€/m2) Specific cost blowers/HTF pumps, salt/HTF HXs (€/m2) Land specific cost (€/m2) Specific cost PB + SG (€/kWe) Specific cost TES: salts + tanks variable (€/kg) Specific cost TES: salt pumps + tanks fixed (€/kWh) Specific cost fossil fuel (€/kWh) Cost of engineering, construction & contingencies (% of Kinvest) Annual specific cost O&M (€/kWhe) Annual insurance rate (%) Effective interest rate (%) Depreciation period (a)

10

Reference STPP

New STPP concept

155 16 8 30 10 2 750 1 10 0.0232 20 0.035 1 7 25

130 30 20 2 45 2 750 1 10 0.0232 20 0.035 1 7 25

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Fig. 9. Comparison between the results of the CO2 model and experimental data from the test facility at the PSA for 27th October 2010: inlet (real) and outlet (real and simulated) temperatures of the collectors’ loop in the upper graph; pressure loss in the collectors’ loop (real and simulated) and mass flow rate (real) in the lower graph; including also the DNI in both graphs.

efficiency of the plant. Fig. 15 shows that the highest value of net annual efficiency is reached with 28 subfields and around 503 °C temperature at the collectors’ outlet. In addition, for temperatures higher than 500 °C the slope of each curve decreases as the number of subfields increases. Since thermal energy storage is more efficient for higher temperature leaps, this effect may be due to a lower proportion of dumped energy for larger sizes of the SF when temperature increases. In order to analyse such influence, Fig. 16 represents dumping factor, defined as the ratio of dumped energy to thermal energy useful to the steam generation train, for each configuration, also including in dashed line the dumping factor for the reference plant. The dumping factor seen in Fig. 16 increases with the number of subfields and, in turn, decreases with the outlet temperature. Although the curves with respect to the outlet temperature for a given number of subfields seem to be parallel to each other, the curve slope is more pronounced when the number of subfields is increased. As a matter of fact, 1.2% difference can be observed in the dumping factor between highest and lowest temperature for 40 subfields whereas the difference is around 0.5% for 23 subfields in the same temperature range.

thermal power, parasitic losses are lower for higher values of the outlet temperature. This effect helps to explain the worse results of net annual production observed in Fig. 13 for low temperatures. Besides, Fig. 14 shows that the relative impact of electric losses decreases with a higher number of subfields, suggesting a better performance for bigger sizes of the solar field in terms of parasitic consumptions. To better assess the optimal temperature in terms of electricity production, weighting the result with respect to the net collection area, it is useful to compare the net annual efficiency of each plant, defined as the net annual electricity production divided by the radiant solar energy available for the SF. Net annual efficiencies are depicted in Fig. 15 for the same cases analysed in Fig. 13. As seen in Fig. 15, for a fixed number of subfields the net annual efficiency shows a maximum between 503 and 513 °C, in accordance to the optimum temperature values observed in Fig. 13. The reasons for such behaviour are related to a balance between SF and PB efficiencies that relies on the temperature dependence explained in Sections 2 and 3. Lower temperature values result in lower PB efficiencies, whereas higher temperatures imply higher thermal losses, as a consequence of Eq. (3), that reduce the SF efficiency and hence the overall net

Fig. 10. Comparison between the results of the reference plant model and real operation data of a commercial STPP with thermal oil for a cloudy day of spring (24th March): inlet and outlet temperatures of the solar field and mass flow rate in the upper graph; gross and net electric power and storage load in the lower graph; including also the DNI in both graphs. 11

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Fig. 11. Results of net electric power, electric losses, storage load and DNI obtained with the model of the STPP using thermal oil and with the model of the new STPP using sCO2 (with 23 subfields and 493 °C outlet temperature) for four days of spring.

Fig. 12. Gross annual electricity production of the reference plant, in dashed line, and the new plant for different values of outlet temperature and number of subfields.

Fig. 14. Electric losses factor (annual electric losses divided by gross electricity production) in the sCO2 plant for different values of outlet temperature and number of subfields, including in dashed line the losses factor of the reference plant with thermal oil.

Fig. 13. Net annual electricity production of the reference plant, in dashed line, and the new plant for different values of outlet temperature and number of subfields.

Fig. 15. Net annual efficiency of the reference plant, in dashed line, and the new plant for different values of outlet temperature and number of subfields.

12

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thermal losses in the solar field than the reference STPP, thus reducing the final efficiency obtained in Fig. 15 for a plant with thermal oil. On the other hand, IberTrough-type collectors using standard receiver tubes with 70 mm outer diameter are expected to show lower values of IAM than the ones considered for 89 mm tubes [19]. Therefore, the breakdown of each factor influencing the final results is not straightforward and it would require specific analyses, out of the scope of this work, to be clearly determined. 6. Conclusions and further work In this work, a new concept of solar thermal power plant with largeaperture parabolic-trough collectors is proposed using CO2 in supercritical state as primary working fluid and molten salts as secondary heat transfer fluid and thermal energy storage medium. A parametric study is performed by means of a simulation model to optimize the expected annual production for such innovative plants as function of the outlet temperature and the net collection area of the solar field, compared to the production of a conventional STPP using thermal oil that is used as reference. The results are promising since 12.48% annual net efficiency is expected for 503 °C of collectors’ outlet temperature, applying the same net collection area for the solar field (513875 m2) as in the reference plant with thermal oil, which shows 12.33%. Nonetheless, the plant efficiency can be increased up to 12.87% by enlarging the solar field, corresponding to a net collection area of 625587 m2. In addition to the performance study, a basic economic analysis is carried out to obtain some overall figures regarding expected savings of the new technology compared to conventional STPPs using thermal oil. As a result, about 6% savings are foreseen in terms of levelized cost of electricity (LCoE) for 714957 m2 of net collection area and 523 °C of collectors’ outlet temperature. However, given the huge uncertainties concerning the cost of required components and financial parameters of solar plants with the innovative technology of sCO2, this analysis is just preliminary and intends to show an approximate figure of electricity cost for the new concept, suggesting possible savings with respect to a reference plant. In order to address the next step in the development of this technology, several technical and economic uncertainties should be investigated and solved with regard to a real implementation: flexible hoses for the interconnections, possible leaks of gas, cold points in molten salt circuits, gas blowers, gas/salt heat exchangers and operation and maintenance costs mainly.

Fig. 16. Dumping factor (thermal energy dumped divided by thermal energy useful to the steam generator) in the CO2 plant for different values of outlet temperature and number of subfields, including in dashed line the dumping factor of the reference plant with thermal oil.

Additionally, the expected savings in terms of startup time for the power block when electricity production lasts for the whole night may also have an influence on annual efficiencies. When the number of subfields increases, the total amount of thermal energy that can be stored in the storage tanks also increases, enabling more hours of daily operation. As a result, for a high number of subfields there is no need to stop the power block every day and its startup curve is avoided, hence reducing the corresponding losses in electricity production. In addition to the results obtained in terms of efficiency it is very useful to consider the expected cost of electricity produced by means of the LCoE calculation method described in Section 3. However, the economic parameters considered in such study involve great uncertainties regarding the cost of components. In this way, rather than establishing accurate values of electricity costs, this analysis intends to reflect the impact of varying the solar field size and outlet temperature on final energy costs, and hence remark the advantages of the new concept by adapting the plant configuration to the specific economic values available at design phase. Fig. 17 represents the relative values for LCoE in the new STPP concept using sCO2 as HTF with respect to the reference STPP with thermal oil. The LCoE obtained for the reference STPP (100% in the yaxis of Fig. 17) using thermal oil as HTF corresponds to 205.6 €/MWhe, similar to the figures obtained in previous works [43]. In Fig. 17, the lowest cost is not given for the same parameters that provided the highest annual efficiency, but it is achieved with a plant configuration of 32 subfields and 523 °C temperature at the collectors’ outlet. The results shown in Fig. 17 seem to reflect the behaviour of the net annual efficiency observed for larger SF sizes in Fig. 15, together with the impact of the TES cost reduction associated to the use of higher temperatures. In this way, optimum temperatures in terms of electricity cost are shifted to the right with respect to Fig. 15. The gains related to a lower energy dumping proportion and lower parasitic losses for increasing temperatures (Figs. 14 and 16) provide decreasing values of LCoE within the range considered, except in the case of 24 subfields which presents a minimum LCoE for 513 °C. Nevertheless, the optimum temperature and number of subfields strongly depend on the specific economic values considered and small changes in such parameters may significantly affect the results. Hence, the values shown in Fig. 17 should be taken as an example of preliminary estimation to analyse expected trends in LCoE variation. The values in Fig. 8, along with the lower specific costs expected for the solar field with large-size PTs considered in Table 3, may suggest that the promising results obtained are exclusively due to the effect of such collectors and are not related to the use of CO2 as working fluid. The better annual efficiency of the new technology may be affected by the higher IAM of large-size collectors, but using such PTs with the same receiver tubes (89 mm) for thermal oil would involve higher

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to

Fig. 17. Relative value of the levelized electricity cost (LCoE) for the new STPP with sCO2 for different values of outlet HTF temperature and number of subfields in the SF with respect to the LCoE for the reference STPP with thermal oil, in dashed line (205.6 €/MWhe). 13

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influence the work reported in this paper.

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