Hybrid solar power plant with thermochemical energy storage: A multi-objective operational optimisation

Hybrid solar power plant with thermochemical energy storage: a multi-objective operational optimisation R.Bravoa,1, C.Ortizb,c, R.Chacarteguid, D.Friedricha,∗ aSchool of Engineering, Institute for Energy Systems, The University of Edinburgh, UK bFacultad de F´ısica, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012, Sevilla, Spain cDepartamento de Ingenier´ıa, Universidad Loyola Andaluc´ıa, Av. de las Universidades s/n, Dos Hermanas, 41704, Sevilla, Spain dDepartamento de Ingenier´ıa Energ´etica, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain Abstract Energy storage is key to decarbonising the energy sector by reducing intermittency and increasing the integration of renewable energy. Thermochemical energy storage (TCES) integrated with concentrated solar and photovoltaic power plants, has the potential to provide dispatchable and competitive energy. Here we develop a multi-objective optimisation framework to find the best operational strategy of a hybrid solar power plant with a TCES system. The model uses a typical meteorological year to optimise one-year hourly operation. The results demonstrate that the integration of a calcium-looping process as TCES in a concentrating solar power plant provides dispatchability and, when hybridised with photovoltaic, enhances its competitiveness with current electricity prices. The low mismatch between supply and demand, even when a fixed commitment is required throughout the year, together with a high overall efficiency, indicates that the integration of calcium-looping in hybrid solar power plants is an opportunity to increase the penetration of solar energy in the power sector. Through the optimisation framework presented, a seasonal energy storage analysis can be developed, although a second optimisation stage is required to improve the sizing of the main components of the system in order to further reduce the energy costs. Keywords: Calcium-looping, Thermochemical energy storage, Hybrid energy systems, Concentrating solar power, Photovoltaic systems, Multi-objective optimisation 1. Introduction Renewable energies are key to enhance the sustainable development and decarbonisation of the power sector, and its agile implementation is required to reduce the negative effects of global warming [1]. Renewable power plants (other than hydropower) have low maintenance and operational costs [2], their carbon emissions are substantially lower compared to fossil fuel power stations [3] and their development is key to energy independence. However, these are not dispatchable (i.e. renewable power plants can dispatch energy just when the resource is available). Some renewable power plants are very competitive, where in some locations, bids for recent auctions have reached prices even below 20 USD MWh−1(mainly based on wind and solar technologies) [4]. The continuous growth in the penetration of renewable energy technologies in the power sector and the natural variability of the resource (e.g. solar, wind) adds large fluctuations in generation and large mismatches with power ∗Corresponding author Email address: [email protected] (D.Friedrich) demand [5]. To reduce variability and increase dispatchability of renewable power plants, the integration of energy storage allows to have control in the power dispatch [6]. Therefore, to increase the penetration of solar technologies in the power sector, the integration of energy storage is essential. On the one hand, in the case of photovoltaic systems (PV), despite the fact that the rate of projects under development is very high, the integration of electric batteries as energy storage is not economically feasible [7], but it could be competitive in the long term if the current high price of large scale electric batteries is reduced considerably [8]. On the other hand, concentrating solar power technologies (CSP) integrated with energy storage are key systems that could provide clean and dispatchable energy [9]. Furthermore, the development of CSP plants integrated with energy storage and hybridised with PV systems give solar technologies dispatchability at competitive costs [10] [11], [12]. In addition, in order to improve the dispatchability and capacity factor of solar hybrid power plants, by integrating a small fossil back-up unit, flexibility is given by allowing some carbon emissions [13], [14]. Different energy storage technologies have been proposed in concentrating solar power plants, based on three different concepts: sensible, latent and thermochemical energy storage. Sensible thermal energy storage is a mature 1The author is supported by a PhD student scholarship from BECAS CHILE, CONICYT. November 15, 2019 technology used in concentrating solar power plants, which works with a temperature difference of a substance, for example, water or molten salts [15]. Latent thermal energy storage uses the heat stored or released during the phase change of a material [16]. Finally, thermochemical energy storage uses the heat of reaction of a reversible chemical reaction that absorbs and rejects energy depending on the operation [17]. Promising thermochemical energy storage technologies that can be integrated into concentrating solar power plants are the calcination-carbonation process of calcium carbonate [18], [19], or magnesium oxide [20]. Whilst TCES systems based on magnesium oxide work at lower temperatures (350-400 ◦C) and are considered interesting processes to use the waste heat from industrial processes [20], TCES based on calcium carbonate works at higher temperatures and is an attractive and more efficient technology to integrate into CSP plants [21]. This process is based on the following reaction that involves calcium carbonate (CaCO3), calcium oxide (CaO) and carbon dioxide (CO2): CaCO3(s)CaO(s)+CO2(g)(1) with ∆ ˆ H◦ r= 178 kJ mol−1[22] The integration of this process, also known as calciumlooping (CaL), as a energy storage system, has several benefits. For instance, because its high energy density, a relatively small storage volume has the potential to operate as long-term energy storage, and the precursor materials used in the process, such as limestone or dolomite, are an abundant, non-corrosive, non-toxic and cheap material [18]. In order to decrease the deactivation of the material due to a multi-cyclic operation, modified materials can be used in the process [23]. In this context [21] compares different materials and conditions to enhance the multicycle CaO conversion. Hence, the integration of a CaL process as thermochemical energy storage (TCES) technology in concentrating solar power plants is a suitable sustainable alternative to provide dispatchable power. In order to evaluate the dispatchability of solar power plants integrated with CaL as a TCES, current studies focus on the simulation of the operation using a typical period to estimate the operation of a whole year [24], [7], for instance, one or two representative days with hourly time steps. Nevertheless, these studies suggest that a one year with hourly time steps simulation is crucial to evaluate the operation of the solar power plant under variable solar irradiation, to consider daily and seasonal variability of the solar resource [24]. According to [25], to define the best operational strategy for a renewable energy system integrated with energy storage, an optimisation study is required, however, the storage system increase the complexity of the problem. Several studies exploit synergies between expensive but dispatchable power plants, such as CSP with thermal energy storage, integrated with affordable but intermittent renewable technologies, e.g. PV [13], [12]. These studies, based on the application of optimisation techniques, focus on the development of operational strategies that minimises and/or maximises different key performance indicators as objective functions. In this context, [13] optimises the operation of a hybrid solar power plant integrated with thermal energy storage in the Atacama Desert, concluding that a multi-objective optimisation routine is crucial to estimate and analyse the trade-off between technical and financial performance. The focus of this research is to find the best operational strategy of a renewable power plant by maximising both the energy supplied and the dispatchability under a specific commitement, two goals that during some periods of the year are conflicting objectives. Consequently, a multi-objective optimisation framework to model a one-year hourly operation strategy of a hybrid solar power plant with thermochemical energy storage is the main focus of the present study. Here we exploit the capacity of linear programming to optimise the annual performance of the power plant, taking into account the daily and seasonal variability of the solar resource. To reach this goal, the CaL process is modelled as mass and energy balances, where the energy balance of each subsystem depends on the temperature and the mass flow rate of the fluid. In addition, the thermodynamic properties also depend on the temperature. To simplify this non-linear model, the temperature of each process will be fixed and defined according to [24]. To handle both objectives, a linear scalarisation method is applied, as discussed in [11]. The results of this multi-objective optimisation method is a Pareto frontier that represents the trade-off between the net energy dispatched (GWh year−1) (that influences the levelised cost of the electricity), and the mismatch between supply and demand, estimated here through the loss of power supply capacity (GWh year−1), that represents the dispatchability of the power plant under a given commitment. Abbreviations DNI: Direct normal irradiation GTI: Global tilted irradiation TMY: Typical meteorological year CSP: Concentrating solar power CaL: Calcium-looping process TCES: Thermochemical energy storage PV: Photovoltaic LCOE: Levelised cost of electricity LPS: Loss of power supply SoC: State of Charge Nomenclature i: subscript, period (hours) k: subscript, material 2 DNIi: direct normal irradiation period i GTIi: global tilted irradiation period i ACSP: solar tower heliostats field area PST: steam turbine capacity PMC: main CO2compressor capacity PMT: main CO2turbine capacity PHPSC: high pressure CO2compressor capacity PHPST: high pressure CO2turbine capacity STOCO2:CO2storage vessel capacity STOCaO:CaO storage tank capacity STOSolids:Solids storage tank capacity APV: photovoltaic field area ηopt: optical efficiency solar field (DNI to receiver) ηreceiver: thermal efficiency receiver Pnet i: net power period i Enet: net energy generated Pdemand i: power demand period i LPSi: loss of power supply period i ˆmi: molar flow rate (kmol/s) ˙mi: mass flow rate (kg/s) ˆ h: molar enthalpy (kJ/mol) h: enthalpy (kJ/kg) MWi: molecular weight, component i ∆ˆ h0 f,i: molar enthalpy of formation X:CaO conversion 2. Methodology and Framework description In this section, the modelling of a CaL thermochemical energy storage process, integrated in a hybrid solar power plant, is presented. Then, a multi-objective optimisation method to define the best one-year hourly operational strategy is described. 2.1. Description Figure 1 represents the process involved in the generation of electricity through the use of a CaL process integrated in a CSP and hybridised with a PV system. The CSP-CaL scheme (and nomenclature) is taken from the base case proposed in [24]. Each stream is represented by a letter and a number, where the letter defines the type of substance (g: CO2; c: CaO; s: solids CaO +CaCO3), and the number indicates the position of the stream in the diagram. For the present study, a Python model has been developed to optimise the operation of a hybrid solar plant with CaL energy storage by mass and energy balances. This model uses real solar irradiation as input, and by linear programming, optimises the annual hourly operation of a defined power plant (CSP with CaL plus PV). Note that the current algorithm optimises the plant operation and not the components sizing; hence, the capacity of each component in this study is an input to the model. The following list summarises the capacities of the main components of the power plant:  Solar Tower field area: ACSP,m2  Steam Turbine capacity: PST,MW  Main CO2Compressor capacity: PMC,MW  Main CO2Turbine capacity: PMT,MW  High Pressure CO2Compressor capacity: PHPSC, MW  High Pressure CO2Turbine capacity: PHPST,MW  CO2Storage Vessel: STOCO2,m3  CaO Storage Tank: STOCaO,m3  Solids Storage Tank: STOSolids,m3  Photovoltaic field area: APV,m2 In the model, the CSP is a solar tower technology that provides heat to carry out the endothermic reaction that splits CaCO3into CaO and CO2at 900◦C, according to equation 1. The location where this reaction takes place is known as calciner and coincides with the solar receiver. Full calcination is assumed in the model [26]. CaO exiting the calciner is stored at atmospheric pressure and high temperature in an insulated tank. The second stream that exits the calciner, consisting of pure CO2at 900◦C, first exchanges heat in a Heat Recovery Steam Generator (HRSG) to produce electricity. Next, the CO2leaves the heat exchanger and cools to approximately 40◦Cto improve the efficiency of the compression process that is occurring afterwards. After the compressor, this stream (now with a pressure of approximately 3 bar) has two possibilities: (i) it can be used in the carbonator to produce the reversible exothermic reaction (carbonation) where it reacts with CaO from the CaO storage tank forming CaCO3and releasing heat according to the previous reaction; (ii) or can be stored at high pressure in a 75 bar vessel, by using a multi-stage compressor. Then, when power needs to be dispatched, this high-pressure stream first drives a turbine to generate electricity and then mixes with the stream flowing from the power loop. This flow is heated in a regenerative system, which reaches around 654◦Cand is then sent to the carbonator to drive the exothermic reaction described above. The CaO conversion (X) in the carbonator is highly dependent on the reactor conditions (pressure, temperature, % v/v CO2) and the CaO precursor used [21]. In this work, a conservative value of X=0.15 is assumed. The heat released from the reaction is taken by the CO2that is present in excess in the carbonator. After that, this pure CO2stream runs a gas turbine (main turbine) to produce electricity that is used to drive the main compressor and the surplus is dispatched to the network. The CO2leaves the turbine at 1 bar and approximately 700◦Cand then it exchanges heat in the regenerative system to increase the temperature of the CO2stream before entering the carbonator. Then, the CO2flow described above is cooled to 40◦Cto be compressed in the main compressor, closing the cycle (see figure 1). 3 Figure 1: Mass and energy flow model of the calcium-looping system 2.2. Energy systems analysis The following section describes the mass and energy balances used in the model for the operation of the main processes of the power plant. The main components are: solar field (heliostats and receiver), reactors (carbonator and calciner), heat exchangers, coolers, compressors and turbines. Main properties for CaCO3,CaO and CO2are summarised in table 1. All the variables described below are non-negative real numbers unless otherwise stated. 2.2.1. Solar field: In the solar field, each heliostat focuses the solar irradiation on the calciner that is located in the top of the solar tower (receiver). The total thermal power transferred and used in the receiver at each time step (Qcalciner i) is calculated according equation 2. QCalciner i=DNIi·ηopt i·ηreceiver ·ACSP −QCurtailment i (2) Where DNIiis the direct normal irradiation, ACSP is the total area covered by the heliostats, ηopt iis the optical efficiency of the solar field that varies every hour in the model and depends on the relative position between the sun, the heliostats and the tower (including losses related to blocking, soiling, reflectance, attenuation, interception and cosine effect [27]) and ηreceiver is the efficiency of the receiver, which is assumed in this work as 0.85 [27]. A sensitivity analysis on this value is carried out in section 4.1. The curtailment (Qcurtailment i) is the power that has to be curtailed when the power cycle is running at full capacity and the storage system is fully charged. 2.2.2. Calciner: The endothermic calcination reaction occurs within the calciner, which in this case coincides with the receiver chamber located in the top of the tower. In this reactor, the stream s2, which contains calcium carbonate and calcium oxide, is heated to drive the calcination. According to [24] to achieve full calcination at amospheric pressure and short residence times, a temperature around 900◦C is required. In the present model, fully calcination is assumed [23]. Hence, because there is no accumulation of energy in the system, nor shaft work, all the heat from the solar field is used to heat the stream s2 and complete the reaction, according to: QCalciner i= ∆( ˆmk,i ·ˆ hk,i)+∆ˆ hr,i (3) with, ∆( ˆmk,i ·ˆ hk,i) = ˆmg1,i ·ˆ hg1,i + ˆmc1,i ·ˆ hc1,i −ˆms2,i ·ˆ hs2,i ∆ˆ hr,i = ˆms2,i ·∆ˆ H◦ r The molar flow rate of CO2(stream g1) is equal to the molar flow rate of CO2produced in the reaction. Finally, the CaO molar flow rate (stream c1) is equal to the molar flow rate of CaO in stream s2 plus the molar flow rate of CaO produced in the reaction. 4 Table 1: Properties of main components ∆ˆ h0 f(kJ/mol) [22] Cp (cal/mol ·K)[28] MW (kg/kmol) [28] CaCO3−1207 19.68 + 0.01189 ·T−307600 ·T−2100.09 CaO −635 10.00 + 0.00484 ·T−108000 ·T−256.08 CO2−394 10.34 + 0.00274 ·T−195500 ·T−244.01 2.2.3. Heat exchangers, heaters and coolers: In a heat exchanger, there is no energy accumulation, and if considered as adiabatic, the amount of heat transferred from the hot fluid (h) to the cold fluid (c) can be modelled by [29]: ˙mhin,i ·hhin,i −˙mhout,i ·hhout,i = (4) ˙mcout,i ·hcout,i −˙mcin,i ·hcin,i However, the model considers thermal efficiencies in heat exchangers. As presented in previous studies [7], electric heaters can be used as heaters to use the excess electricity when supply exceed commitment. In the case of cooler 4, the CO2stream exiting the recuperator HXG (g12) is cooled from 150◦Cdown to 40◦Cand part of this heat is used to heat up the CO2coming from the storage (Heater 1). Heater 2 was included in the process in order to avoid a non-linear relation in the carbonator, and its electrical consumption is included in the operational electrical consumption of the power plant. Coolers are modelled similarly to heat exchangers (no energy accumulation, no shaft work, adiabatic), the difference here is that the working fluid cools while a refrigerant is heating (air in this case). The energy balance for coolers is described as: ˙mr,i ·cpr·∆Tr,i = ˙mhin,i ·(hhout,i −hhin,i) (5) Where cpris the specific heat capacity of the refrigerant (cp,air (23◦C, 41% rel. humidity)= 1.012 kJ/kg ·K[22]) 2.2.4. Superheated steam Rankine cycle: In order to simplify the model, the turbine power output (ST) of the Rankine cycle is simulated as a linear relation with the heat absorbed in the heat recovery steam generator (HRSG) according to: PST i=QHRSG i·ηSSRC (6) where ηSSRC is the global efficiency from thermal to electrical power. Based on models and results analysed by using the commercial software ASPEN PLUS, an efficiency ηSSRC = 0.268 will be considered in this study. 2.2.5. Compressors and turbines: The following relations are used to estimate the total work in turbines and compressors according to [30]: ∆( ˙mihturb,i) = ˙mi γi γi−1 Pin,i ρin,i    1−Pout,i Pin,i  γi−1 γi   ηs (7) ∆( ˙mihcomp) = ˙mi γi γi−1 Pin,i ρin,i   Pout,i Pin,i  γi−1 γi−1   ηs (8) where γis the heat capacity ratio, used here as the isentropic expansion factor, and ηsis the isentropic efficiency of the turbine or compressor. 2.2.6. Carbonator: In the carbonator, the reverse reaction of the calciner occurs. In this reactor, pure CaO from the CaO storage tank is combined with CO2from the CO2storage cycle to produce CaCO3and heat (with a conversion of 15%). After the carbonator, while the resulting solid stream (CaO+ CaCO3) is stored in the solid storage tank, the CO2stream (presented here in excess to absorb the heat released in the reaction) is first conducted to a turbine to produce electricity, then to a heat exchanger to use part of the heat available in the regenerative system, finally to a cooler and compressor to close the cycle. 2.2.7. Storage tanks: The three storage components (CaO and solids storage tanks, and the CO2storage vessel) are modelled by mass balances. Where the density under storage conditions considers internal porosity and particle packing density of the material, as described in [24]. Here the state of charge (SoCiin m3) is defined as the volume of material that is present in the tank in period i, which is equal to the state of charge of the previous period plus the input minus the output flows during the current period (in m3), according to the following expressions: SoCi(m3) = (SoCi=0(%) ·STOcapacity(m3),if i= 0 SoCi−1+ ( ˙min −˙mout)·∆t·1 ρi, i ≥1 (9) In our model, the state of charge (in percentage) for each tank at the start of the operation (i=0) is defined as: SoCi=0 =     100% CaO tank 0% Solids (CaO +CaCO3) tank 100% CO2vessel (10) 5 This means that during the operation of the first hours, the storage tanks of the thermochemical energy storage system are fully charge, which allows the plant to dispatch energy even without solar irradiation. This is just a criterion for the simulations, which has insignificant influence in the yearly results. In the operational optimisation routine, to calculate the actual net energy dispatched, it is necessary to estimate the difference between the available energy in the initial and final periods of the annual operation. To calculate this difference, an average energy density factor (ξ) is calculated as the rate between net power dispatched and CaO mass flow rate that feeds the carbonator: ξiMW h tonCaO =Pnet i(MW ) ˙mc2(kgCaO s)·3600( s h)·1 1000 (ton kg )(11) The results of the model were analysed along the year to estimate this rate and a specific power production value of ξi≈0.053 MW h tonCaO −1was calculated. 2.2.8. Photovoltaic power plant: Finally, the photovoltaic power plant converts the solar irradiation (in this case, the total irradiance received on a plane with fixed tilt) that reaches each solar module into electric power by the photovoltaic effect. In the simplified model shown in figure 1, the power flows to the inverter and then is dispatched to the grid. According the model described in [11], the total efficiency of the PV plant, from the solar irradiation to the electric power, considers the efficiency of panels and inverters, in addition with the losses related with module mismatch, connections and wiring. 2.3. Key performance indicators In order to compare the operational strategy of different configurations based on measurable results, the following are key indicators for technical and financial performance used in this study:  Enet is the total net electric energy dispatched by the power plant in one year of operation.  LPSC is the total loss of power supply capacity during one year of operation, and LPSP is the loss of power supply probability according to: LPSC =XLPSi(12) LPSP =LPSC PCommitment i·8760 (13)  ECommitment is the electricity dispatched to fulfil the commitment .  EExcess is the electricity dispatched when the net energy exceeds the commitment (in this model there is no restriction for the maximum power dispatched).  ECurtailed is the amount of energy available in the heliostat solar field that has to be curtailed when the power plant is running at full capacity and the storage tanks are fully charged.  ∆Ef−iis the energy difference between the last hour and the first hour of operation. This difference is used to calculate the net electricity dispatched during one year of operation.  ¯ PNet is the average power dispatched in one year, according to: ¯ PNet =ENet 8760 (14)  PMax is the maximum power dispatched during at least one hour, over one year of operation.  CF CSP is the capacity factor referred to the CO2 Brayton cycle [31], where Enet,Brayton Cycle is the total energy dispatched by the Brayton cycle during one year of operation, and Pmax,Brayton Cycle is the maximum power dispatched. CF CSP =Enet,Brayton Cycle Pmax,Brayton Cycle ·8760 (15) Two estimations for efficiencies will be calculated:  ηCSP,Rec is the efficiency of the solar tower power plant considering the energy available and used in the calciner: ηCSP,Rec =PENet,CSP i PQCalciner i (16)  ηCSP,DNI is the overall efficiency of the solar power plant considering the solar energy available in the solar field: ηCSP,DNI =PENet,CSP i PDNIi·ACSP (17)  Levelised cost of the energy: representing the present value (considering an annual interest rate of r= 7%) of the total life cycle costs (TLCC) involved in the generation of each unit of energy during the lifetime of the power plant (N= 25 years) [32]. LCOE =TLCC ENet ·r 1−(1 + r)−N(18) 2.4. Operational optimisation by linear programming The main objective of this research is to model one year of operation (8760 timesteps), considering the hourly solar resource of a typical meteorological year. In order to linearise the equations presented above, the temperatures of the processes are fixed, according to the parameters and results presented in [24], were non-linear models are used to simulate the operation of the CSP plant with CaL. In 6 a power plant, this may be possible by the instrumentation engineering, through the definition and control of the temperatures of each process. Hence, the operational optimisation routine optimises the mass flow rate of some streams and calculate those that are dependent (because there are direct relationships between some streams) in order to optimise the hourly operation. Optimisation objectives can be defined according to user preferences, and these can be easily changed in the model. In this study, for a fixed power plant, the objectives of the operational optimisation are defined by:  Maximisation of the net energy supplied during one year of operation (typical year), where the hourly net power dispatched is defined by: PNet i=PGenerated i−POwn consumption i(19)  Minimisation of the loss of power supply (LPS), which estimates the mismatch between the energy supplied and the commitment, i.e. the net power to be dispatched by the power plant, according to the following equation: LPSi=(PCommitment i−PNet i, PCommitment i> PNet i 0,otherwise. (20) 2.5. Scalarisation method In order to handle both objectives, and according to the results presented in [11], here a linear scalarisation method is implemented. The model developed in [11], which optimises the annual operation of a hybrid solar power plant with energy storage, found that the linear scalarisation method works faster than the epsilon () constrain method, obtaining the same Pareto frontier. The only precaution is to choose a suitable scaling factor (ω) to scale the second objective (section 3.3 presents the analysis to define the value of ωfor the case study described below). Therefore, the function that describes the multi-objective optimisation problem in the present study is: maximize I X i=1 {PNet i·∆ti−w·LPSi·∆ti}(21) 2.6. Computer system and tools All optimisations presented in this study were performed using the following resources:  PC: Intel Core i7-6700 CPU @ 3.4GHz, 16 GB RAM.  Operating system: 64-bits Windows 10 Education.  Programming language: Python 3.5.3 [33]  Optimisation package: Pyomo 5.6.1 [34], [35]  Solver: Gurobi 8.1.1 [36] 3. Case Study To evaluate the model and compare the results with published data, the power plant under analysis will be located in Seville, Spain. Here public data available for Seville is used (≈N 37.4◦W 6.2◦, elevation 72 m), in the ”Photovoltaic Geographical information system” (PVGIS project) of the European Commission Joint Research Centre [37]. 3.1. Input data 3.1.1. Technical parameters To run the model, the following hourly annual input data is required:  Direct normal irradiation (DNI)  Optical efficiency solar field (ηopt)  Global tilted irradiation (GTI) In the present study, the typical meteorological year (TMY) is used as a representative year. Then, the direct normal irradiation is used to model a solar tower plant in SAM 2019 [27] to estimate the hourly optical efficiency of the heliostat field of the solar tower system. While values of hourly optical efficiency during summer days are from 0.42 to 0.6, winter day values are between 0.3 to 0.55, and the annual average value (¯ηopt) is around 0.53. According to the previous equations and relations, the model also needs a series of technical and financial parameters. Among the technical parameters necessary to run the model are: efficiencies of each component (from [27]), thermodynamic properties of the elements (from table 1), and operational temperatures and pressures of each subsystem from [38]. In addition, the model considers thermal efficiencies and heat losses in the carbonator and heat exchangers. Storage tanks are modelled by mass balances, and heat losses are considered according to the design of the tanks, i.e. the insulation of the storage tanks is designed to achieve a heat transfer coefficient in the order of 100 W m−2, and its losses are included as electrical consumption of the power plant. 3.1.2. Financial parameters Financial parameters used in the model are investment costs (IC) and operational and maintenance costs (O&MC) of the solar tower, the CaL system and the photovoltaic system. The capital cost of the heliostat field, the solar tower and the photovoltaic system were obtained by modelling both a solar tower power plant and a photovoltaic system in SAM [27]. Then, the estimate of the total land area and cost (using a value of 25000 USD/ha) was used from these simulations. Capital costs for the calciner (here the investment cost was increased by 10% to include the connections necessaries to install it in the solar tower receiver), carbonator, compressors, turbines, and other major components for the CaL system are summarised in table 2 where the average exchange rate considered was rexch = 1.18 (EUR USD, 2018) [39]. For the 7 calciner and carbonator, equations 2 and 22 are used to estimate the thermal power in order to calculate the scaling parameter applied in the equation for investment cost: QCarbonator =QCalciner ·ηoverall,th (22) where ηopt ≈0.53, ηreceiver = 0.85, DNIdesign = 0.95 kW/m2, Qcurtailment = 0, and ηoverall,th = 0.9. Finally, a contingency of 7% and an EPC (engineering, procurement and construction) cost of 13% were considered [27]. In addition, to include all other components and auxiliary systems, a balance of plant of 10% was used. The last necessary input data is the hourly power that the power plant have to dispatch: Pdemand i. This is used to calculate the loss of power supply (LPSi) as a metric to estimate the reliability or dispatchability of the power plant under that commitment. 3.2. Validation Aspen PlusT M In order to validate the model, different configurations (based on [24]) were evaluated using Aspen PlusT M and optimised by our model written in Python. Table 3 compares three different cases, which shows the mass flow rate of different streams (kg s−1) and the energy conversion in turbines, compressors, and heat exchangers (MW). In the table, the three sections in the first row indicate: the thermal power available in the calciner (MWth), solar multiple (SM) as described in [43] and CaO conversion in the carbonator (X). As can be seen in the table, in most of the values, the difference between the values obtained through the Python and Aspen models is less than 1%. 3.3. Linear scalarisation method, definition of ω In the present study, as shown in table 4, different optimisation routines with different ωwere evaluated (according section 2.5). Table 4 shows that an ω= 1 is a suitable scaling factor. This can be explained because the units of both objectives are the same and both have the same order of magnitude in each operation time step. In addition, in the present model there are no penalties or cost for energy not served. In other cases, for instance, when the cost associated with unserved energy is greater than the cost of energy generation, a large scaling factor may be more appropriate. 3.4. Solar Power Plant Design According figure 1, to optimise the annual operation of the power plant, the equipment sizes have to be known. This section presents a process to estimate the capacities of each main component using the equations and relationships described above. In a future study, this method will be improved by defining a second optimisation stage (similar to the design optimisation routine by genetic algorithms developed in [13]). To establish a case study, it is necessary to define the capacities of the main components of the solar power plant. The process starts with the definition of the expected average power dispatched by the CSP+CaL system. In this case, a capacity of 15 MW is defined. Then, according to the estimated global efficiency value reported in [24] (ηCSP,Rec = 0.321), it is possible to estimate the average power needed in the calciner: ¯ Qcalc ≈47MWth. Next, using the equation 2 modified to take into account the average thermal power available in the calciner (¯qcalc) per square meter of heliostat field, it is possible to have an estimate value for the heliostat aperture area (ACSP ): ¯ QCalc =ACSP ·¯qCalc = 47,000 kW (23) where ¯qCalc =P8760 1ηopt i·ηreceiver ·DNIi 8760 ≈0.1089 kW m2 (24) By using SAM [27] for the simulation of solar tower plant located in Seville, the average thermal power in the receiver per square meter of heliostat reflective area is approximately 0.1032 kW/m2. Hence, ACSP ≈430,000 m2 Then, with this solar field aperture area, the design capacity of the calciner is calculated considering the equation given above (with ¯ηopt ≈0.53, ηreceiver = 0.85, DNIdesign = 0.95): Qcalc,design ≈180 MWth After that, in order to find the capacities of each component mentioned in section 3.4, this thermal power is used as input in the Aspen model (Qcalc = 180 MWth), and the following capacities for each components were obtained: PST ≈10 MW PMC ≈23 MW PMT ≈43 MW PHPSC ≈10 MW PHPST ≈2MW Then, a number of storage hours can be defined to combine with the specific power production defined above, to estimate the capacity of the CaO storage tank (with ρCaO ≈3370 kg/m3[44], and values of porosity and packing density of solids equals to 0.5 and 0.6 respectively). For instance, with 20 hours of storage: ξi,P = 0.053 MW h tonCaO =15 MW ·20 h STOCaO ·ρCaO →STOCaO ≈5650 m3 Now, considering the following properties in the storage tanks: ρCaCO3≈2700 kg/m3[44] (porosity = 0.5) and 8 Table 2: References for estimating CaL components Component Scaling parameter Investment cost (IC) in MUSD Ref. Calciner Thermal Power (MWth) IC= (13140 ·Q0.67 calc ·10−6)·rexch [40] Carbonator Thermal Power (MWth) IC= (16591 ·Q0.67 carb ·10−6)·rexch [40] Steam power cycle Cycle gross capacity (MWe) IC= (290 + 1040) ·PST max ·10−6[27] Heat exchangers area (m2) and pressure (bar) IC= (2546.9·A0.67 HE ·P0.28 HE ·10−6)·rexch [40] Cooling towers Thermal Power (MWth) IC= (32.3·Qcool ·10−3)·rexch [40] CO2compressors and turbines - See reference for calculation procedure [40] CO2storage vessel - See reference for calculation procedure [41] Solids storage tanks - See references for calculation procedure [42], [41] Table 3: Validation Aspen PlusT M 100MWth, SM=3 33MWth, SM=1 100MWth, x=0.3 item unit Aspen Python Aspen Python Aspen Python s2 kg/s216.6 215.8 72.2 71.6 125.6 125.2 c2 kg/s64.6 64.3 64.6 64 33.9 33.8 g9 kg/s133.9 134 133.8 134.4 132.6 132.7 g13 kg/s126.2 126.5 126.2 126.8 124.6 124.7 ST MW 5.8 5.8 1.9 1.9 6.1 6.1 MC MW 12.9 12.8 12.9 11.5 12.8 12.7 MT MW 23.9 24 23.9 24 23.6 23.6 HPSC MW 5.3 5.3 0 0 5.6 5.6 HPST MW 0 0 0 0 0 0 HXG MW 75.9 75.8 75.9 76 75 74.8 PNet MW 8.2 8.2 11.3 12.5 9.3 9.3 Table 4: Scalarisation method Objective unit ω= 0 ω= 1 ω→ ∞ Enet∗GWh year−1118.2 117.6115.6 LPSC GWh year−124.6 21.018.9 ρCO2≈762 kg/m3, a CaO conversion X=0.15, an estimate of the capacity in m3of the two other tanks can be calculated as a ratio of STOCaO, where Vm,i is the molar volume of substance i, defined as the volume occupied by one mole of component i in the storage tank or vessel, by the following relationships: Vm,i =MWi ρi (25) STOSolids =ST OCaO ·x·Vm,CaCO3 Vm,CaO + (1 −x)(26) ≈5735 m3 STOCO2=STOCaO ·x·Vm,CO2 Vm,CaO ≈875 m3(27) Finally, according to section 2.5, the model was evaluated with ω= 0 to maximise the energy dispatched and the capacities of all components indicated above. By the operational optimisation routine, it was calculated that the total net energy delivered in one year is 118.4GWh, and the average power dispatched is 13.5MW. Therefore, for the following calculations, the power commitment will be defined as Pcommit i= 13.5MW, ∀i. 4. Results and Analysis To compare the results of different designs, nine configurations were analysed, which are summarised in table 5. The estimated capacities above are shown as ”Base Case” configuration. The columns of table 5 show the name given to the configuration (Base Case, A to H), then the aperture area of the heliostat field, the power capacity of the steam turbine, the main compressor and turbine capacities, next, the capacities of the high pressure compressor and turbine, columns 8 to 10 show the capacities of the storage tanks, and finally, the photovoltaic solar field area. In each row, different designs are presented, which are related to the Base Case, and all the configurations have the same aperture area of the heliostat field. For example, in configuration A the capacity of each component was increased by 20%, while in configuration B by 50%. Compressors and turbines of configuration C increased by 50% and storage remains the same. Capacities of the storage systems in configuration D were multiplied by 3. Configuration E, F, 9