Organic Rankine Cycle (ORC) technology is widely considered for various applications, including geothermal energy [1
], biomass [2
], waste heat recovery [3
] and the production of electricity through the utilization of solar thermal energy, due to its suitability for operation at small power capacities and relatively low temperatures below 300 °C, in which the conventional steam-Rankine cycle is technically infeasible or not cost-effective. Solar ORCs are oriented toward grid-connected or distributed generation (i.e., to cover the electricity demands of isolated industrial consumers or in the context of community mini-grids) [4
] as well as desalination [5
] and irrigation [6
] applications. In contrast to more mature photovoltaics (PV), the key advantage of solar ORCs is their capability for cost-effective thermal energy storage (TES), which comes at a lower cost than electrochemical batteries [7
]. The cost-effective energy storage of solar ORCs can also make them more profitable as dispatchable power sources in the renewable energy-dominated landscape. Considering the above, the investigation of their thermodynamic and economic performance becomes increasingly significant.
Up to date, several thermodynamic and techno-economic studies on the simulation and optimization of solar ORCs have only considered their nominal design points. One of the first studies following this approach was conducted by Tchanche et al. [8
], who investigated different fluids for low-temperature solar ORCs and highlighted the importance of different evaluation criteria that need to be taken into account during the selection process. A study of similar scope was carried out by Delgado-Torres and García-Rodríguez [9
], who evaluated the on-design performance of low-temperature (<145 °C) solar recuperative ORCs driven by flat plate collectors (FPCs). The authors highlighted the overall superior performance of dry fluids, with isopentane, R245ca, R245fa and isobutane featuring the minimum solar collector areas per produced kWe
of electrical output. A study of similar scope but focusing on a concentrated solar power (CSP) standard and recuperative ORC with a power capacity of 20 kWe was carried out by Ferrara et al. [10
]. The authors compared the performance of three fluids: R134a, R245fa and acetone. For the latter, a cycle efficiency of 20% was calculated (recuperative ORC). Finally, the authors suggested that piston expanders are the most suitable expander technology, due to the capability of handling low fluid rates and high-pressure ratios. Other studies follow similar approaches but put more emphasis on novel configurations and components. For example, Shahverdi et al. [11
] investigated the installation of an Archimedes screw turbine in the heat transfer loop of a solar ORC driven by parabolic trough collectors (PTCs), considering different working fluids. In this study, two types of absorbers were evaluated, consisting of smooth and corrugated tubes. The best performance in terms of net power as well as cycle (25%) and total efficiency (about 17%) was obtained by R113, while the corrugated tube absorber was superior. Deligant et al. [12
] assessed the potential of using a standard radial turbine as an expander in a solar ORC by conducting computational fluid dynamics (CFD) simulations, which indicated that isentropic efficiencies of up to 78% were achievable.
Another topic that is widely investigated is the performance of solar cogeneration (combined heat and power-CHP) and trigeneration (combined cooling heat and power-CCHP) systems including ORCs, which come in different varieties, depending on the employed cooling technology, which can be (among different solutions) a vapor compression cycle (VCC) [13
], an absorption chiller [14
] an adsorption chiller [15
] or an ejector-based cycle [16
] in different configurations. Some indicative examples are presented in the following. Jafary et al. [17
] investigated a PTC-driven system consisting of two different types of ORCs (recuperative and regenerative) and an absorption chiller. The overall energy and exergy efficiencies of the systems were 93.35% and 12.69% (recuperative) and 80.66% and 6.64% (regenerative system). Khaliq et al. [18
] investigated a system including an ORC and a hybrid cooling cycle involving an absorption chiller and an ejector device and examined the influence of different design parameters on the energetic and exergetic performance. In a particular scenario in which isobutane was considered as the ORC working fluid, the overall energy and exergy efficiencies were 65.42% and 13.98%, respectively. Braimakis et al. [19
] evaluated the thermodynamic and economic performance of a hybrid solar-biomass trigeneration system based on the combination of an ORC and a VCC. The authors reported ORC thermal efficiencies between 3.7% and 10.05% for different organic fluids and conditions, while the cogeneration efficiency could be as high as 73.5% resulting in a payback period of 12.3 years.
Several studies have considered the off-design operation of solar ORCs, which is of high significance due to the daily and seasonal variability of solar radiation. In these studies, off-design simulation models for the solar collectors, storage tank and ORC equipment components (heat exchangers, expanders, pumps) are developed and interconnected, while different control strategies are defined to determine the operational mode of the system under different solar availability and energy demand scenarios. In this way, the operation of the solar ORC is simulated under variable heat input from the solar collectors (usually considering an hourly time step) and its performance is assessed based on its operation throughout a particular period (daily, seasonal or annual).
Baccioli and Desideri [20
] developed a dynamic simulation model of a solar ORC operating with R600a driven by compound solar collectors with a maximum heat transfer fluid (HTF) temperature of 140 °C. A sliding-velocity control strategy was assumed for the ORC, which, according to the authors, could drive the plant without requiring a thermal energy storage system (TES). In another study, Wang et al. [21
], implemented a genetic algorithm (GA) based methodology for optimizing recuperative solar ORCs driven by FPCs under variable solar radiation. The authors concluded that the best daily performance was obtained by working fluid R123, which had a daily energy efficiency of 7.59% at a maximum cycle temperature of 69.84 °C. Freeman et al. [22
] investigated the working fluid selection and thermodynamic optimization aspects of a domestic solar ORC for CHP production. The ORC was driven by evacuated tube collectors (ETCs) of a 15 m2
area, while the temperature of the HTF was varied from 90 °C to 240 °C. When considering a standard, single-stage collector configuration, the authors concluded that the optimal system resulted in an annual work output equal to 955 kWh/year. Furthermore, the authors additionally evaluated a modified configuration that included a two-stage solar collector array which, owing to its improved efficiency, could lead to a 12% increase in the annual work output. In both cases, R245ca was found to be the optimal working fluid. Kutlu et al. [23
] investigated the off-design performance of a small-scale solar ORC equipped with a pressurized hot water storage tank and driven by an ETC field of 500 m2
with a nominal maximum hot water temperature of 110 °C. The power output of the ORC, which operated with R245fa, varied between 4.3 kWe and 11.2 kWe throughout 24 h, while its efficiency ranged from 7.6% to 9.2%. Petrollese and Cocco [24
] introduced a thermodynamic and techno-economic optimization approach for large-scale solar recuperative ORCs operating with linear Fresnel collectors (LFCs) of a total area of 8500 m2
, operating with a nominal HTF temperature equal to 275 °C and considering the use of three different working fluids, hexamethyldisiloxane, toluene and n-heptane. The off-design modeling approach was based on the definition of a probability distribution of multiple operating scenarios including different HTF mass flow rates and temperatures as well as ambient temperatures. Among the examined working fluids, toluene led to the lowest levelized cost of electricity (LCoE), which was equal to 122 €2019/MWhe
, while also having a cycle efficiency of 19.5%. Casartelli et al. [25
] investigated different off-design control strategies for a 5 MWe
solar ORC driven by LFCs featuring maximum HTF temperatures of 390 °C and 310 °C and operating with toluene. Among the two investigated control strategies (sliding pressure and fixed pressure-partial admission at turbine inlet), the second resulted in higher electrical power output and efficiency. Patil et al. [26
] carried out a techno-economic performance comparison between a PV (with and without battery storage) and a PTC-driven ORC system having a nominal power capacity of 50 kWe. The authors concluded that while the stand-alone PV (capacity factor 0.27) had the overall lowest LCoE (0.12 USD2018/kWhe
) when a higher capacity factor (0.56) was considered, the LCoE of the solar ORC (0.19 USD2018/kWhe
) was lower than that of the PV-battery module (0.26 USD2018/kWhe
). Li et al. [27
] also evaluated the off-design performance of a solar ORC driven by CPCs and highlighted the importance of proper TES sizing to minimize dynamic resonance phenomena.
Most studies on small-scale solar ORCs focus on low- or mid-temperature applications featuring flat plate and evacuated tube collectors with nominal cycle temperatures below 150 °C. As a result, the thermodynamic and techno-economic performance of micro- and small-scale solar ORCs driven by concentrated solar collectors such as parabolic trough and dish collectors, which enable their more efficient operation at higher temperatures, has not been thoroughly evaluated. Furthermore, in most techno-economic studies on solar ORCs, only their on-design performance is assessed, while their off-design operation, which is of high importance considering the intermittent and variable nature of solar energy, is neglected. Finally, in many studies, the optimization of key design variables of solar ORCs is not undertaken, as their goal is only the simulation/evaluation of system performance under different scenarios.
Aiming to address the aforementioned research gaps, the present work aims at the systematic techno-economic optimization of high-temperature solar ORCs driven by PTCs and parabolic dish collectors (PDCs), considering their off-design, annual performance in five European cities, namely Athens, Madrid, Rome, Brussels and Berlin. The selection of these cities was based on their climate classification according to the Köppen-Geiger climate specification [28
]. More specifically, since the cities are located in southern and central Europe, they are associated with sufficient annual direct solar irradiation, which is necessary for the cost-effectiveness of the proposed solar ORC (Table 1
). Regarding the southern cities, all of them are characterized by a Mediterranean climate. However, while Rome’s climate is standard Mediterranean, Athens and Madrid have hotter and colder semi-arid climates, respectively. Meanwhile, Berlin and Brussels have Marine West Coast climates. The selection of cities with different climate characteristics helps to examine the impact of climate on system performance and profitability. As a matter of fact, Madrid and Athens exhibit the highest annual direct normal irradiance, while the corresponding value for Brussels is almost three times less and slightly lower than in Berlin.
The off-design performance of the solar ORC is evaluated with the development and integration of a series of off-design models for all equipment components (solar collectors, thermal energy storage tank, heat exchangers, expander, pump, motor/generator) to accurately simulate their operation under realistic, variable conditions. Furthermore, cost correlations based on literature data and manufacturers’ datasheets are used for capital and operational cost estimation. In each case, a GA optimization technique is implemented to determine the optimal solar field area and storage tank capacity with regard to the maximum annual total solar energy conversion efficiency and minimum LCoE of the solar ORCs. GA optimization belongs to the larger class of evolutionary algorithms, which are based on Darwin’s theory of evolution [29
]. Nowadays, this optimization method is applied with many variations to numerous engineering problems and has been used on several occasions for the thermodynamic and technoeconomic optimization of ORC systems of various configurations and types [30
All results are available in the Supplementary Materials
of the present publication. The Pareto fronts of the solutions produced by the GA are shown in Figure 5
. The shape of the fronts illustrates that there is a trade-off between the optimization criteria of efficiency and LCoE [88
]. Indeed, the energy efficiency maximization and the LCoE minimization are independent and in certain cases conflicting objectives. For example, a small-sized system may achieve high annual solar conversion efficiencies, but the produced electricity may not necessarily be sufficient to compensate for its investment cost, negatively affecting its cost-effectiveness. Regarding the investigated solar ORC, increasing the area of solar collectors enables the ORC to operate closer to its nominal point (and hence at higher thermal efficiency) for longer periods, leading to an increase of the total solar thermal conversion efficiency. However, the increased generated electricity does not necessarily compensate for the higher cost of the solar field. Accordingly, increasing the storage tank volume extends the capacity factor of the system and results in increased solar thermal conversion efficiencies, but the increased cost of the tank may lead to disproportionately increased capital costs and have a negative influence on the LCoE.
The above point is illustrated more clearly in Figure 6
, which presents the optimization results for an indicative scenario of Athens with PTCs for all the examined working fluids. In this figure, the variation of the two optimization objectives (ηtot
and LCoE) with respect to the two optimization variables of the system (Acol
) is illustrated.
3.1. Total Energy Efficiency
It can be observed that higher total conversion efficiencies are obtained in northern cities (Brussels and Berlin) compared to southern cities (mainly Athens and Madrid). Since in all cases the nominal size of the ORC is the same, due to the lower solar availability in Northern cities, the ORC directly exploits the harvested solar energy. On the contrary, in Southern cities, a large share of the harvested solar heat is stored and eventually lost to the ambient. Furthermore, the lower ambient temperatures in Northern cities lead to lower solar collector losses.
It can be observed that the use of different working fluids does not lead to substantial differences in efficiencies. Generally, Cyclohexane tends to achieve the highest performance, followed by Cyclopentane and Isohexane. In most cases, Toluene appears to yield slightly inferior efficiencies followed by Benzene. The overall maximum efficiency achieved in the studied cities lies between 10.5–11%. These values are, in general, lower than those reported in similar studies. This can be mainly attributed to the fact that the present work takes into detailed account different types of losses, including the heat losses to the ambient, pump, inverters’ and generators’ losses, which are often underestimated or even neglected.
Finally, it can be observed that, although PDCs lead to slightly higher efficiencies compared to PTCs, the difference in the performance of systems operating with these two types of collectors is insignificant.
The influence of the geographical location on the LCoE is much more significant than its influence on the total conversion efficiency. As already mentioned, for southern cities, the available solar energy is higher, leading to higher power generation and enabling system operation for more hours annually and closer to nominal conditions. The increased electricity generation results in increased cash inflows and reduced LCoE values, improving the economic viability of the system. More specifically, in the case of Athens and Madrid, which represent the financially optimal results, the cost of electricity for the PTC-Cyclopentane scenario is close to 0.34 €/kWh, whereas the corresponding LCoE in Brussels is 0.9 €/kWh.
In the majority of the scenarios, the optimal financial outcome is achieved by the fluids that yield the highest efficiencies, as Cyclopentane and Cyclohexane exhibit the highest profitability, whereas Toluene, Benzene and Hexane are associated with lower cost-effectiveness. Since the fluids are hydrocarbons and have similar prices, their costs do not lead to substantial differentiation in their economic competitiveness, which is mainly ruled by their thermodynamic performance and equipment sizing and, hence, costs.
From an economic perspective, PTCs are more favorable, since they have almost the same energetic performance but come at a lower cost than PDCs.
4.1. Interpretation of Optimization Results
An overview of the results is presented in Table 11
, in which the combinations of optimal solar field areas and storage tank capacities with regard to efficiency and LCoE for each city are shown.
As it can be observed in Figure 6
, the collecting surface appears to be negatively correlated with both ηtot
and LCoE. When the surface is too small, the useful solar heat is reduced. As a result, the harvested solar energy is fully used directly for driving the ORC, while the stored heat and thus storage tank energy losses are minimized. On the other hand, as the surface is increased, although more solar energy is harvested, a part is left unexploited and eventually lost to the ambient from the storage tank due to the fixed nominal size of the ORC.
Accordingly, for smaller collector areas, the annually generated electrical energy is lower because the system is operational for fewer hours, resulting in a decreased cashflows and increased LCoE. On the contrary, for larger collector areas, the ORC operates for longer periods at higher efficiencies, producing more electrical energy and thus the LCoE is reduced.
As shown in the figures, the solar field area corresponding to the optimal economic performance is around 150 m2. For larger areas, the improvement in the economic competitiveness of the system is negligible, since the CAPEX is increased while the electrical energy generation remains almost constant. This region is not depicted in the diagrams since it corresponds to both minimized efficiency and financial performance.
Concerning the volume of the storage tank, it is positively correlated with the energy efficiency, since higher volumes result in increased system operating hours and thus higher energy exploitation. However, given a specific collecting area, an increase in the storage capacity beyond a specific value does not offer any more benefits and even increases the CAPEX, resulting in a stall of economic and energy efficiency.
Additionally, it can be observed that the optimal results are concentrated in a range of relatively small storage tank capacities. This is justified both in terms of efficiency as well as in terms of economic performance. It is obvious that the higher storage tank volumes increase the CAPEX, while at the same time they increase the thermal inertia of the system. Larger tanks would demand much higher thermal power from the collectors to increase their temperature since they contain larger quantities of HTF and have greater ambient losses. Therefore, even though the inspected range is between 0.2–5 m3, in all cases the derived optimal points correspond to tank capacities below 1.2 m3. Another reason for this behavior is justified by the selection of the heat losses coefficient of the tank. The value considered in this study corresponds to a medium-insulated tank, hence for high temperatures the heat losses are not negligible. If high insulation is considered, the total energy efficiency is expected to increase for the same tank size; however, this would lead to a significantly higher tank cost and may have either an either neutral or a negative impact on the LCoE.
Generally, the lowest LCoE values are attained in the southern cities, where the solar availability, and thus the total electrical energy generation, are higher.
Based on the results, it can be concluded that a major hindrance to the commercial uptake of the investigated solar ORCs is their limited financial viability. As shown in the table, the optimal LCoE for the examined cities ranges between 0.34–0.91 €/kWh. Meanwhile, as of 2019, the LCoE in the EU of PV technology, the main competitor to the investigated solar ORC concept, ranges from 0.0619 to 0.32 €/kWh [89
], as illustrated in Figure 7
, being considerably lower than the LCoE of the solar ORC.
Furthermore, the LCoE of the solar ORCs is much higher than the current electricity prices listed in Table 9
. Of course, it should be noted that in the study, no policy incentives (such as subsidies or premiums) have been taken into account, which are very commonly introduced in RES systems and which could greatly improve the economic competitiveness of the investigated solar ORCs. Moreover, it is expected that the addition of heat production by recovering low-temperature heat from the condenser could enhance the cost-effectiveness at a small penalty of the ORC thermal efficiency. This is mainly because the condensation temperature is already relatively high due to the technical limitations of the expander’s pressure ratios and therefore, under the current design, the cooling water outlet temperature is suitable for floor heating applications.
To provide a more detailed analysis of the system economics, the contribution of the cost of different components into the CAPEX is illustrated for the scenario that yields the economically optimal results of Athens for PTC and using Cyclopentane (as shown in Table 11
) in the two pie charts of Figure 8
. At this point, it has to be mentioned, according to Figure 8
b and the specific costs of the HTF reported in Table 8
, that the selection of Therminol VP-1 has a significant impact on the total costs, owing to the large quantity of the HTF used in the solar field. The use of this particular HTF is necessary due to the high solar field temperatures, which prohibit the use of less expensive HTFs such as ethylene or propylene glycol aqueous mixtures.
Among the ORC components, the biggest cost contribution is that of the screw expanders, followed by the evaporator and pump. When the total system cost is considered, more than half of its cost corresponds to the ORC module, with the solar field also having a strong contribution to the CAPEX.
4.2. Operational Improvements
In order to explore the economic viability of the designed system and determine its capability of achieving lower LCoE values, its economic performance under different nominal evaporator heat duties is presented. The analysis is only carried out for the case of a PTC-driven solar ORC in Athens operating with Cyclopentane, which corresponds to the minimum LCoE scenario. Four additional cases were examined regarding the nominal duty of the evaporator: 25 kW, 32.5 kW, 60 kW and 80 kW. In Figure 9
and Table 12
, the optimal solar field area and storage tank volume for each nominal evaporator heat duty and corresponding LCoE and ηtot
For a given driving temperature, as the evaporator’s heat duty decreases, the ORC power output is decreased. However, the lower accumulation of stored heat (for a given solar field area and storage tank volume) allows for a higher level of charging and therefore the ORC is operational for longer operating hours, thus achieving higher total solar energy conversion efficiencies. On the other hand, because of the decreasing size of the system, the specific investment cost of the equipment components is increased. Ultimately, the negative effect of the increasing specific investment cost is more significant than that of the increased operating hours, as indicated by the increasing LCoE for decreasing nominal evaporator heat duties.
As expected, there is a positive correlation between the optimal solar field area and the ORC nominal power output; as the ORC power scale increases more heat is required, respectively. However, a reverse behavior is observed for the storage tank volume. This can be attributed to the substantial costs of a larger storage tank and the respective additional HTF costs, which push the optimization algorithm toward lower storage tank capacities. In fact, in all cases shown in Table 12
and Figure 10
, the optimal economic performance occurs at low tank capacities. As the profit by sold electricity was not considered to vary within the day, it is more economically efficient to directly consume the solar harvested energy. In this perspective, the storage tank is mostly used to provide the required thermal inertia in the system to allow it to operate at steadier and closer to nominal conditions and therefore 200–300 lt are sufficient.
By observing the trends of Figure 10
, it can be deduced that a further increase in the system scale accompanied by an increase in the collecting surface could eventually lead to even lower LCoE values. However, further increasing the evaporator heat duty beyond this value would require a qualitative change of the considered equipment components (i.e., heat exchangers, expander, pump) and would be outside the scope of the present work, which is oriented toward smaller system scales.
4.3. Comparison of Results to Relevant Studies
In order to properly establish the undertaken optimization procedure, a comparison to similar analyses is carried out. In particular, techno-economic studies oriented towards small-to-medium scale (below 2 MWe
]), exclusively solar-driven, medium-to-high temperature (above 150 °C) ORC systems are taken as reference. The summary of the non-exhaustive comparison is reported in Table 13
, where LCoE values are converted to 2020 equivalent values accounting for inflation rates. It is also stressed that in these studies, similar climates in terms of solar irradiance were investigated, thus neglecting the effect of climate on the results.
As shown, the hereby obtained LCoE (0.343 €/kWh) is higher than most of the others, yet within an acceptable range. First and foremost, it is apparent that economies of scale exist, leading to substantially lower cost of energy in medium-scale systems. In addition, this cost discrepancy is further explained by the different system layouts and operation, as well as the conditions (heat source and heat sink temperature, power range) and assumptions made, such as the economic terms (years of evaluation and discount ratio) and the simulation strategy. Namely, the very low LCoE reported by Sun et al. [91
] is mainly attributed to the overestimation of ORC efficiency (15.26%) and the assumption of constant-efficiency ORC operation throughout the evaluation period. On the other hand, the very high LCoE presented in the study of Ciocolanti et al. [92
] is expected, as it refers to a very small-scale prototype which, additionally, is intended for CHP operation and, as a result, a large amount of the available heat is utilized for heating purposes.
Moreover, the comparative works of Desai et al. [93
] and Petrollesse and Cocco [94
] highlight the importance of TES in the economic feasibility of such systems thanks to the increased operating time. In this context, as shown in the 1 MWe system of Desai and Bandyopadhyay [90
], the operation without TES diminishes the positive effect of economies of scale resulting in similar cost with systems of lower capacity. Ultimately, the 50 kWe system proposed by Patil et al. [26
] attained a low LCoE thanks to the combination of increased system’s capacity factor (0.56) and low storage cost.
Concluding, the reported cost has derived from an optimization analysis of a system incorporating TES using detailed off-design modeling to properly estimate the net produced electricity. Furthermore, present cost values were included covering all types of the system cost. Hence, it appears that the achieved LCoE is acceptable and could be further reduced in a larger-scale application.