Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems

Equation Chapter 1 Section 1 Trabajo Fin de Grado en Ingeniería de las Tecnologías Industriales Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems Autor: Javier Venzalá Higueras Tutores: José Manuel Guisado Falante; Ricardo Chacartegui Ramírez Ramr Dpto. de Ingeniería energética Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2025 iii Trabajo Fin de Grado en Ingeniería de las Tecnologías Industriales Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems Autor: Javier Venzalá Higueras Tutores: José Manuel Guisado Falante Ricardo Chacartegui Ramirez Dpto. de Ingeniería Energética Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2025 v Trabajo Fin de Grado: Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems Autor: Javier Venzalá Higueras Tutores: José Manuel Guisado Falante y Ricardo Chacartegui Ramírez El tribunal nombrado para juzgar el Proyecto arriba indicado, compuesto por los siguientes miembros: Presidente: Vocales: Secretario: Acuerdan otorgarle la calificación de: Sevilla, 2025 El secretario del Tribunal vii A mis abuelos Por enseñarme la palabra “Constancia” ix Agradecimientos En primer lugar, me gustaría mostrar mi más sincera gratitud a mi tutor José Manuel, el cual me ayudó a elegir un trabajo fin de grado acorde a mis intereses dentro de la energía nuclear, así como una plena disponibilidad a lo largo de estos meses permitiéndome mejorar continuamente la calidad de este trabajo; Trabajar con José Manuel me ha permitido mejorar tanto personal como profesionalmente aprendiendo múltiples razonamientos energéticos así como el uso de distintos programas y herramientas informáticas de una manera más completa. Es por esto, entre otros muchos motivos, que expongo mi más sincero agradecimiento por su manera de guiarme al igual que su trato personal en el ámbito académico que me ha permitido dedicarle tanto tiempo a este trabajo. A mi círculo más cercano, tanto dentro como fuera de mi familia, que me ha apoyado incondicionalmente, a lo largo de estos 4 años de carrera, así como a las personas que he conocido este último año, gracias por hacer todo más sencillo. 4.1 Equations and Considerations for part-load analysis 26 4.1.1 Turbines 26 4.1.2 Heat Exchangers 27 4.1.3 Pump 28 4.2 Analysis of performance and results obtained in different scenarios 28 4.2.1 Mass rate 28 4.2.2 Turbine 29 4.2.3 Reactor analysis 31 4.2.4 Overall efficiency 31 5 Off-design smr exergy analysis 33 5.1 Variable load SMR exergy analysis 33 5.1.1 Exergy destruction low-pressure turbine 33 5.1.2 Exergy destruction high-pressure turbine 34 5.1.3 Exergy destruction preheater 1 35 5.1.4 Exergy destruction preheater 2 36 5.1.5 Exergy destruction preheater 3 37 5.1.6 Global analysis at minimum load value 38 5.2 Ambient temperature exergy analysis 39 5.3 Exergy analysis of operation pressure 40 5.3.1 Low-pressure turbine 40 5.3.2 High-pressure turbine 41 5.3.3 Preheater 1 42 5.3.4 Preheater 2 43 5.3.5 Preheater 3 43 5.4 Variation of thermodynamic parameters of the steam cycle 44 5.4.1 Inlet turbine Pressure 44 5.4.2 Live Steam Temperature 46 5.5 Conclusions and discussions 48 6 SMR exergy optimization 51 6.1 Base improvements 51 6.1.1 Live Steam Temperature 51 6.1.2 Low turbine extraction pressure 52 6.1.3 High turbine extraction pressure 53 6.2 Base optimization 54 6.3 Complementary exergy optimization 55 6.4 Conclusion 57 7 References 58 xvii TABLE OF CONTENTS Table 1 Coal-fired electricity production by country (%) 3 Table 2 National production of electricity from natural gas sources (%) (2023) 4 Table 3 Overall installation performance according to the technology used 7 Table 4 Demand covered by nuclear energy in 2022 15 xix LIST OF FIGURES Figure 1 Evolution of the price of electricity in Germany, France and Italy and gas in Europe (€/MWh) [1] 1 Figure 2 GWh of electricity generation in Spain in 2023 (%) 9 Figure 3 Grams of CO2 equivalent per KWh produced according to the technology 9 Figure 4 Part-Load efficiency of a gas turbine in DG systems [43] 12 Figure 5 Part-load efficiency of an alternative combustion engine in DG systems [43] 12 Figure 6 Exergy efficiency of a combined cycle under part-load operation [44] 13 Figure 7 Percentage of exergy destruction by combined cycle equipment 1[45] 13 Figure 8 Percentage of exergy destruction by equipment Combined Cycle 2 [46] 14 Figure 9 PWR technology central scheme 16 Figure 10 Energy equivalence between different raw materials 18 Figure 11 Forecast of annual uranium demand (Year 2040) 18 Figure 12 Selected SMR installation diagram 20 Figure 13 Sankey's diagram of exergy destruction operating under rated design conditions 25 Figure 14 Variable load effect on pump performance 28 Figure 15 Variation of mass rate with load rate 29 Figure 16 Turbine efficiency variation with load rate 29 Figure 17 Variation specific work turbines with load rate 30 Figure 18 Total work output of the turbines vs. Load rate 30 Figure 19 Variation of heat required in the reactor with load rate 31 Figure 20 Efficiency variation of the SMR nuclear power plant under different load rates. 32 Figure 21 Specific exergy destruction low-pressure turbine as a function of load rate 33 Figure 22 Variation percentage of destruction exergy low-pressure turbine as a function of the load rate 34 Figure 23 Specific exergy destruction by high-pressure turbine as a function of the load rate 34 Figure 24 Variation percentage of exergy destruction in high-pressure turbine as a function of the load rate 35 Figure 25 Specific exergy destruction preheater 1 as a function of the load rate 35 Figure 26 Percentage variation of exergy destruction preheater 1 as a function of the load rate 36 Figure 27 Specific exergy destruction preheater 2 as a function of the load rate 36 Figure 28 Percentage variation in exergy destruction preheater 2 as a function of the load rate 37 Figure 29 Specific exergy destruction preheater 3 as a function of the load rate 37 Figure 30 Percentage variation of destruction exergy preheater 3 as a function of the load rate 38 Figure 31 Sankey's diagram of exergy destruction under rated design conditions 38 Figure 32 Variation in percentage of exergy destruction as a function of ambient temperature 39 Figure 33 Specific exergy destruction low-pressure turbine as a function of P [13] 40 Figure 34 Specific exergy destruction low turbine as a function of P [14] 41 Figure 35 Specific exergy destruction low-pressure turbine as a function of P [15] 41 Figure 36 Specific exergy destruction high-pressure turbine as a function of P [10] 42 Figure 37 Specific exergy destruction high-pressure turbine as a function of P [11] 42 Figure 38 Specific exergy destruction preheater 1 as a function of P[14] 43 Figure 39 Specific exergy destruction preheater 2 as a function of P[13] 43 Figure 40 Specific exergy destruction preheater 3 as a function of P[10] 44 Figure 41 Variation of work produced as a function of the inlet turbine pressure 45 Figure 42 Exergy variation destruction by elements as a function of inlet turbine pressure 46 Figure 43 Variation of work produced as a function of the live steam temperature 46 Figure 44 Variation of total produced work as a function of the live steam temperature 47 Figure 45 Variation in the overall efficiency of the installation as a function of the live steam temperature 47 Figure 46 Exergy variation destruction by elements as a function of live steam temperature 48 Figure 47 Exergy efficiencies as a function of load rate 48 Figure 48 Distribution of Exergy for Loads of 1 and 0,6 49 Figure 49 Specific exergy destruction variation by component and total with system load 49 Figure 50 Relationship between the fraction of charge, the exergy destruction and the total turbine work 51 Figure 51 Relationship between live steam temperature, exergy destruction and total turbine work 52 Figure 52 Relationship between P [13], the exergy destruction and the total turbine work 52 Figure 53 Relationship between P [14], exergy destruction and total turbine work 53 Figure 54 Relationship between P [10], the exergy destruction and the total turbine work 53 Figure 55 Relationship between P [11], exergy destruction and total turbine work 54 Figure 56 Analysis of exergy improvements base optimization 54 Figure 57 Analysis of improvements to power base optimization 55 Figure 58 Relationship between P [15], exergy destruction and total turbine work 55 Figure 59 Analysis of exergy improvements complementary optimization 56 Figure 60 Analysis of improvements to complementary power optimization 56 xxi Glossary DG Distributed generation CC Combined cycle Cogen Cogeneration i.e. In other words ORC Organic Rankine Cycle DLN Dry Low Nox ∝ Proportional to GT Gas turbine ICE Alternative combustion engine PWR Pressurized Water Reactor PHWR Pressurized Heavy-Water Reactor LWGR Light Water Graphite Reactor CANDU Canada Deuterium Uranium GCR Gas-Cooled Reactor IAEA International Atomic Energy Agency 𝑊𝑒𝑖 Specific work output 𝛼𝑖 Mass rate 𝜀𝑖 Effectiveness 𝜂𝑖 𝐸𝑥𝐷𝐻𝑃𝑇 Efficiency Exergy destruction high-pressure turbine 𝐸𝑥𝐷𝐿𝑃𝑇 Exergy destruction low-pressure turbine 𝐸𝑥𝐷𝑃𝐻1 Exergy destruction preheater 1 𝐸𝑥𝐷𝑃𝐻2 Exergy destruction preheater 2 𝐸𝑥𝐷𝑃𝐻3 Exergy destruction preheater 3 1 GENERAL OVERVIEW OF POWER CYCLES 1.1 Introduction Currently, the electricity system is at a critical point in terms of energy justice, sustainability and accessibility worldwide, the scope of multiple agreements such as the Paris Treaty, drawn up on December 12, 2015, reflects the importance of countries to address climate change. These policies aim to limit the temperature increase in this century to a maximum of 2ºC, and in turn try to bring this increase value close to 1.5ºC [1] .On the way to new electricity generation systems, it can be seen that they are not only necessary for reasons of environmental preservation, but also in the current situation in which Europe finds itself, clearly marked by a direct dependence on certain energy production systems as well as on their raw materials; an example of this situation is the escalation in the price of gas, which saw an increase in its price due to the pandemic and which was continued to record highs as a result of the international conflict of the war in Ukraine. Figure 1 Evolution of the price of electricity in Germany, France and Italy and gas in Europe (€/MWh) [1] This entails the need to employ inframarginal technologies; that is, technologies which, due to their production characteristics and existing market failures, set the price floor as the lowest-cost or most economically efficient sources of energy generation, something that Chaves J commented as “These high prices hurt consumers across Europe when they are not covered by long-term contracts, and they also produce very high benefits for inframarginal technologies (i.e. those cheaper than natural gas combined cycles), such as renewables or nuclear, again, when they are not committed to long-term contracts [2].” On the other hand, it has been shown that energy efficiency, when there are conflicts and great political General overview of power cycles 8 incorporating various technologies. These include the installation of gas turbine inlet air cooling systems, which increase air density and improve the efficiency of the combustion process, as well as heat recovery systems, which allow waste thermal energy to be harnessed to generate additional electricity, thus increasing the overall thermal efficiency of the system.[24] 1.4 Comparative Exergy Analysis of Power Generation Technologies On the other hand, although it is highly dependent on the electrical power for which the plant is designed, an analysis of the differences in terms of exergy can provide the reader with an insight into the substantial differences between the various technologies; exergy represents the real potential of a form of energy to be transformed into useful work when interacting with its environment. Unlike an energy analysis, it takes into account losses due to irreversibilities and allows the thermodynamic efficiency of a process to be evaluated. If we begin by analysing gas installations with similar power ratings, we can see that they have total exergy efficiencies of around 33%. This could be due to the existence of the combustion chamber, or the air-fuel ratio introduced, both of which have a significant effect on exergy efficiency.[25] In the case of combined cycle, much higher exergy efficiency is observed, with values close to 46% in a 420 MW plant. This improvement is due to the integration of systems that reuse waste heat from the gas cycle to generate more electricity through a steam cycle, which significantly reduces exergy destruction compared to conventional systems. [26] Coal and nuclear power plants have very similar energy and exergy efficiencies, with values of 36% and 37% for coal, respectively, and 30% for both types of nuclear energy. Exergy losses in both cases are highly influenced by emissions and other irreversibilities of the process, which account for around 10% of total losses.[27] Hydroelectric plants with a capacity of 280 MW have high exergy efficiency with an operating range of 6370%. It is estimated that around 30% of exergy is destroyed and cannot be avoided. This loss is mainly related to physical and geographical limitations, such as water height and flow, which determine the efficiency of the system.[28] As far as solar systems are concerned, they show low exergy efficiency compared to other technologies. The solar thermal collector has only 4.4%, while the photovoltaic system reaches 11.2% and the hybrid collector improves to 13.3%. These figures reveal the large amount of exergy destruction, which shows that, despite the energy potential of these sources, the lack of technological development and efficiency of current systems keeps them well below the exergy efficiency of other energy alternatives, as seen above. [29] In wind energy systems, exergy efficiencies of around 40% can be achieved at low wind speeds, and efficiencies of 55% at high wind speeds; these are high efficiency values compared to their competitors. Finally, in the case of biomass, among the many types of technology currently in use, analysis has shown that the chemical exergy of algae biodiesel is similar to that of conventional diesel and petrol, and with some improvements it could be a good option unlike other types of biomass such as wood, agricultural or industrial biomass.[30] 1.5 Overview of the Spanish Electricity Market Once the analysis of the advantages and disadvantages of the different technologies has been made, as well as a brief analysis of the different ranges of exergy efficiencies, we will proceed to make a general view of the situation in Spain, where the energy mix is characterized by having multiple technologies, each with a different percentage and interest. [31] 9 9 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems Figure 2 GWh of electricity generation in Spain in 2023 (%) As can be seen, Spain is a country with a wide variety of natural resources to exploit, so a change in the price of a resource does have an impact, but not as significantly as it might in other countries that do need alternatives to traditional combined cycle or coal-fired power plants, which have a major environmental impact due to their direct dependence on raw materials such as natural gas or coal. Apart from this, we can see a direct impact on CO2 emissions, which is directly proportional in facilities that use this type of resource[32]: Figure 3 Grams of CO2 equivalent per KWh produced according to the technology As can be seen by comparing both graphs, the installation that produces the most power and emits the least CO2 in the process is wind energy. The major drawback is that, in the quest for energy justice, this option does not always guarantee a certain amount of energy to the consumer, as it depends on the external conditions of the environment in which it is located. General overview of power cycles 10 Therefore, one of the most interesting options in this regard would be nuclear energy, which, after wind power, best meets both conditions. In fact, in 2014, nuclear production in Spain prevented the emission of 40 million tonnes of CO2. [33] 1.6 Current and future electrical power distribution Currently, electrical energy, as mentioned above, is in a constant increase in demand, this added to a globalized distribution of energy causes multiple companies and sectors to look for new ways to obtain energy autonomously and self-sufficiently. 1.6.1 Distributed generation systems In this scenario, distributed generation (DG) systems become more important, i.e. small-scale systems that can ensure, whenever possible, the production of energy from different points which, overall, cover demand and at the same time are capable of ensuring the supply of energy to the area or sector. The International Council on Large Electric Systems (CIGRE) defines distributed generation as " All generators with a maximum capacity between 50 MW and 100 MW, connected to the electrical distribution system, and which are not designed or dispatched centrally. The latter implies that distributed generation is not part of the network operator's control", i.e. although the owner of these systems can sell part of the energy produced and feed it into the grid, it is not owned by the electricity company. This type of system has multiple advantages in terms of production, but it also has drawbacks in other areas. In terms of distribution, as Lopes J pointed out, "The development of DG requires the availability of a network to receive DG production. This can be difficult if DG development occurs in remote areas. When solving this problem, issues such as the location of the plants and the level of energy and power expected to be produced can be identified." [34]. Nevertheless, it is advisable to support the demonstration and commercialisation of decentralised renewable energy production technologies. This has multiple advantages, such as the use of local energy sources, greater security of local energy supply and lower energy transmission losses. Such decentralisation also promotes community development and cohesion by facilitating sources of income and creating jobs at the local level.[35] According to many studies, the future of electricity generation will become increasingly decentralised, mainly due to the increase in renewable energy systems such as solar and wind power, complemented by the installation of other smaller-scale generation facilities.[36] 1.6.2 Technological problems of DG systems Distributed electricity generation systems offer significant advantages over centralised generation systems and energy transmission and distribution systems. High prices hurt consumers across Europe unless long-term contracts are established. At the same time, these conditions have generated extraordinary profits for inframarginal technologies, in other words those with lower generation costs, such as renewable sources and nuclear energy.[37] On the other hand, with the increase in energy consumption, the need to improve the capacity of long-distance transmission lines becomes vital. To avoid this dependency, where long distances lead to numerous transmission and distribution losses, it is necessary to build more energy production systems close to the ends of the network, as well as generation close to consumption. The capacity of long-distance transmission lines is increasing, as is the electricity grid's dependence on foreign networks. Therefore, it is necessary to build power plants at the ends of the grid and in consumption centres. This will reduce the need to transfer large amounts of energy over long distances, decrease transmission and distribution losses, strengthen the local electricity grid, and improve the stability of the electricity system.[38] It is vital to analyse the context and situation when increasing the existence of distributed generation systems, because variability in losses and voltage increases throughout the network can cause problems if their 11 11 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems implementation is not properly analysed.[39] Even so, implementing these systems is no easy task, as distributed generation negatively affects the stability of the electrical system due to its low inertia caused by variable demand and control. This is why distributed generation systems whose surpluses are fed into the grid can have a negative impact. 1.6.3 Uses and applications of DG systems In certain global situations and casuistry, distributed energy as a main system is not viable, it is estimated that in Africa approximately 621 million people did not have access to electricity in 2014, this is equivalent to 70% of the population at that time; The situation has not improved and the world population is increasing as well as the need to increase energy production. That is why distributed generation systems, in the absence of potential infrastructures and networks, can be the solution to supply areas that without electricity could not continue to advance towards a better future.[40] The rather large increase in distributed generation observed in the world is largely associated with the progress of low-power generation technologies and government support measures for renewable energy sources; Distributed generation enables the sustainable development of areas with low electricity demand, where centralized energy supply is too expensive. In Russia, the installed electrical capacity of DG systems has reached 37 GW and the contribution to the country's electricity industry is very significant: approximately 13.7%.[41] On the other hand, one of its interests is military use, as well as national protection. In situations where the network is vulnerable due to the possibility of attacks, these systems play a key role, as they can supply electricity to remote areas that in some situations could be left without strategic supply. Another point of interest, from an environmental perspective, is that with the increase in these distributed electricity generation systems, it is possible to reduce the use of conventional power plants that pose serious risks to human health due to their emissions. These systems (DG) are being studied for their potential use with green technologies, which would allow for a significant reduction in impact in the event of a notable increase.[42] 1.6.4 Operation under off-design conditions of DG systems One of the most interesting aspects to study in distributed generation systems is the efficiency and performance of the installation when operating under non-design conditions. In many applications, these systems do not have the capacity to dump excess energy into the grid, which requires them to be able to adapt to the load; this situation is accentuated when DG systems are autonomous or partially connected to a small electrical grid system; in these scenarios, a large change between demand and production can cause major failures, as well as significant instability. This is due to the low electrical inertia of these systems, unlike centralised electricity grids, such as a national grid, where high inertia helps to dampen frequency variations and maintain system stability. If we compare how the efficiency of these systems varies when the load varies, we can see how efficiency drops and losses increase at lower load percentages. On the other hand, the system is capable of adapting to demand, which makes it more reliable and safer in the situations mentioned above. If we analyse the situation of gas turbines from different studies, we can see how efficiency declines when the load percentage varies. Furthermore, we can see that at very low load percentages, the slope becomes more pronounced, which is why the operating range, depending on the turbine, is not complete, i.e. there are values for which the turbine does not operate. It can be seen that by using the three turbines, 70% can be set as the point from which efficiency declines most rapidly, and therefore it may not be worthwhile to operate under lower load General overview of power cycles 12 conditions. Figure 4 Part-Load efficiency of a gas turbine in DG systems [43] On the other hand, if we analyse the efficiency of alternative internal combustion engines, we can see that they follow the same trend and that, in general, it is clear at a glance that for different technologies, efficiency decreases as the load percentage decreases. Figure 5 Part-load efficiency of an alternative combustion engine in DG systems [43] That is why, when working with this type of system operating under off-design conditions, it is necessary to study the minimum operating load percentage for each installation that does not worsen the machine's performance and allows for good efficiency in different demand scenarios. 13 13 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems 1.6.5 Exergy analysis of DG systems under off-design conditions. If an exergy analysis of a combined cycle is performed as an example, it can be observed that when these systems operate at part-load, regardless of the choice of temperature control method, the exergy efficiency declines. This is due to an increase in the exergy destruction that is generated in the different equipment that make up the cycle. Therefore, when varying the load percentage, not only the performance and features must be analysed, but also the appropriate efficiency parameters such as exergy efficiency. Figure 6 Exergy efficiency of a combined cycle under part-load operation [44] Figure 7 Percentage of exergy destruction by combined cycle equipment 1[45] On the other hand, exergy losses in power generation facilities using this type of technology can be seen to be concentrated mainly in combustion equipment or recovery chambers. This is consistent with what has been observed in most exergy analyses of combined cycles, where combustion and energy transfer processes represent the critical points in terms of energy irreversibilities. The exergy analysis reveals that there are significant sources of exergy destruction, especially in processes where there are large temperature differences General overview of power cycles 14 or chemical reactions. Figure 8 Percentage of exergy destruction by equipment Combined Cycle 2 [46] If we analyse how the efficiency of this equipment varies when operating under variable load conditions, we can see that the equipment that destroys the most exergy, when operating at reduced load levels, increases its losses considerably, which leads to an increase in the percentage of exergy destruction by this equipment in the installation. Equipment such as combustion chambers or turbines take on greater importance due to the variability of the thermodynamic properties of the flows. That is why, in installations that operate under variable loads, the exergy aspect is very important due to the considerable increase in losses and the decrease in the exergy efficiency of individual equipment, which leads to greater total exergy destruction. 2 NUCLEAR ENERGY 2.1 Current situation of electricity generation through the use of nuclear energy Nuclear energy plays a fundamental role in decarbonisation. In terms of volume, nuclear energy is the most powerful source of energy. Renewable energies, such as solar, wind, hydroelectric, geothermal, tidal and hydrogen, produce zero greenhouse gas emissions compared to fossil fuels. However, the production and use of these renewable energies has been increasing, but it is not enough to meet the demand of all sectors worldwide.[47] Clean energy is being incorporated into the energy system at an unprecedented rate, with an increase of more than 560 gigawatts (GW) of new renewable generation capacity during 2023. [48] Even so, their deployment remains uneven, both in the technologies used and between countries, the costs of most clean technologies are resuming a downward trend after the increase experienced as a result of the Covid-19 pandemic due to the increase in the price of other sources such as traditional fuels. This supports the growth of renewable energy generation capacity, which will increase from the current 4,250 GW to almost 10,000 GW in 2030 according to the STEPS scenario. [48] Despite the existence of certain periods when nuclear energy research and production may seem close to its end, nuclear energy production is on the rise globally. Nuclear energy production worldwide had a capacity of 205, 2710 and 2790 Twh in 1973, 2018 and 2019, [49] respectively, where we observe an energy that continues to increase. The IAEA's highest projection for nuclear capacity reaches 950 GW (net) in 2050, a positive difference of 2.5 times from the installed nuclear capacity in 2023. [50] If a global overview is made, we can see the impact that certain countries have in terms of energy generation and demand covered, you can see [51] how the countries that contribute the most and defend nuclear power manage to cover a large part of the electricity through this method; These countries, each with a different consumption, in terms of power, achieve a very high demand covered, we can highlight: Country Demand covered (%) Belgium 46,4% Bulgaria 32,6% France 36,7% Hungary 47% Slovakia 53,1% Ukraine 55% Table 4 Demand covered by nuclear energy in 2022 It is worth adding the situation of countries such as Spain that are currently at a midpoint due to the changes taken by energy policies, in this study it can be seen how 20.3% of the electricity demand in Spain was covered by nuclear, although currently this percentage has been reduced. Nuclear energy 16 But how is this energy obtained? What are the methods currently used? , although this energy generation depends mainly on the country, most countries are committed to PWR Nuclear Power Plants, which represent 77.9% of the reactors currently operating in the world [51], the rest of the reactors are mainly older of the PHWR or LWGR type, even so if we take a look at the technologies with which the new nuclear power plants are being built, we see that most countries are betting on this type of reactors again, 88.8% of the reactors under construction are PWR. [51] 2.2 Operation of a PWR type nuclear power plant Without going into the installation of this type of plant, they mainly have the following agents: [52] • Primary circuit: Mainly made up of equipment such as the Pressur, the Reactor Vessel, the fuel, the control rods... In this part of the facility, the energy produced by the nuclear reactor that produces steam is transformed and heated to optimal conditions for subsequent heat exchange. • Secondary circuit: This second part of the secondary circuit is really the one that is responsible for the generation of electrical energy, it has a block of water pipes that thanks to the heat exchanged with the primary circuit converts water back into saturated steam, this steam goes directly to the turbine that thanks to an alternator transforms mechanical energy into electricity. • Auxiliary elements: These are elements that do not directly influence the generation of electricity, but are key to the installation, we can highlight two mainly: o Tertiary circuit: The tertiary circuit depends mainly on the source or the external medium with which the heat exchange is carried out, that is, the steam that is used in the turbine must be sent again at the beginning of the secondary circuit and for this it must exchange heat with an external environment such as the sea, a river (including the famous cooling towers) or the use of equipment such as air condensers that are responsible for recovering the steam that comes out of the turbine and turns it into liquid water and at the right temperature. As mentioned above, it mainly depends on the type of installation we use. o Containment Building: A vault-shaped element usually composed of concrete and is responsible for protecting the reactor mainly, or the part of the primary circuit that contains radioactive elements, this vault prevents, in the event of an accident, the emission of radiation, as well as protecting the reactor against external attacks. Figure 9 PWR technology central scheme 17 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems 2.3 Small modular reactor (SMR) In all this scenario, the need arises to find a technology that covers everything mentioned above so far, that is, a clean technology in terms of gas emissions, a technology that can supply the growing demand for electricity, as well as ensure production in a decentralized way to ensure price stability due to international policies that affect both supply and obtaining of certain raw materials. In this case, a new line of study arises within the field of Nuclear Energy, SMR type reactors, this type of reactors should be noted that they would work in a complementary way in a different type of market and scenario than those previously studied, that is, the objective and demand covered by these reactors is not related to the situation of traditional large-scale reactors. which, as we have mentioned before, are still being built today. 2.3.1 General characteristics and trends Small Modular Reactors (SMRs) are reactors with a capacity, due to their smaller size, to operate at part-load and on demand, ensuring that they are a complementary option that works together with renewable energies, ensuring that they cover unmet demand scenarios or scenarios where they hardly have to provide energy. These reactors are under study and would have a capacity of about 300 MW per unit; Despite being an interesting option, these reactors still have to go through controls, existing standards, emergency tests, provision and preparation of the respective control rooms; In other words, the cost of capital per unit is lower than that of current reactors, but their competitiveness remains to be demonstrated [53] On the other hand, it should be noted that due to their small size and advances in this type of technology, apart from simplicity, construction, operation and affordability, this type of reactors offer greater safety by eliminating most of the main causes of accidents, such as the large pipes used in the primary circuit.[54] We are going to initially comment on the types of SMR and the most typical technologies that are being studied, these technologies are according to the IAEA: • Land-based and water-cooled SMRs: There are currently 14 designs of ground-based water-cooled SMRs (LWRs or HWRs). • Water-cooled seawater SMRs: there are 6 designs of these reactors, which operate in a similar way to the previous ones but located in fleets that offer flexible deployment options; the countries that are betting the most on this type of reactors are China, the Czech Republic and the United States. The first SMR of its kind is owned by the Navy of the Russian Federation and has been commercially operated since May 2020 with a nuclear power capacity of 70 MW(e) and supplies heat and electricity to the city of Pevek in the Chukotka region.[55] • Gas-cooled SMRs: With around 14 types gas-cooled and reaching temperatures above 750°C, there are two test reactors that have been in operation for several years (one in Japan and one in China). • Liquid metal-cooled fast neutron SMRs: About 10 reactor designs with this technology operate with metals such as sodium, pure lead, or eutectic lead-bismuth. The most significant advances are the BREST-OD-300 reactor being built in Russia and France, although we also have sodium-cooled reactors in the United States. • Molten salt SMR: Currently with 11 designs, these reactors provide increased safety, high efficiency, and flexible fuel cycles. These reactors are in the design phase in countries such as Denmark, France, the United Kingdom and the United States. • SMR micro reactors: this type of reactors operate with various refrigerants depending on the type and operate up to a maximum of 30 MW. Its function is to cover market niches, remote areas, and disaster areas where the supply of electricity is complicated. There are currently thirteen designs in development. With all this we find a scenario of 68 active designs, of which 22 are water-cooled reactors (WCRs) and 46 that operate with another coolant (N-WCRs). Development of the cycle under rated design conditions 24 24 𝑊𝑒𝑝𝑢𝑚𝑝𝑠[𝐾𝐽 𝐾𝑔]=𝑃5−𝑃4 (10∙𝑒𝑡𝑎𝑝𝑢𝑚𝑝𝑠)=1 (21) As can be seen, the consumption by the pump is minimal, which is why it will not be included in the final expression of the respective performance calculation. Once the specific work has been obtained, we can calculate the performance of our power cycle, due to the great difference that exists between the power consumed by the pumps, we will only include the work of the turbine η𝑜𝑣𝑒𝑟𝑎𝑙𝑙[%]=𝑊𝑒𝑇𝑜𝑡𝑎𝑙𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑊𝑒𝑟𝑒𝑎𝑐𝑡𝑜𝑟 ∙100 (22) η𝑜𝑣𝑒𝑟𝑎𝑙𝑙[%]=33,19 (23) Finally, as we previously set the total power at 150 MW, we will be able to obtain the steam flow rate that must circulate through our cycle. 150∙103=𝑊𝑒𝑇𝑜𝑡𝑎𝑙𝑡𝑢𝑟𝑏𝑖𝑛𝑒 ∙ 𝑚𝑑𝑜𝑡𝑚𝑎𝑥∙𝜂𝑚𝑒𝑐 (24) 𝜂𝑚𝑒𝑐[−]=0,95 (25) This results in a maximum flow obtained of: 𝑚𝑑𝑜𝑡[𝑘𝑔 𝑠]=265,9 (26) 3.4 Exergy analysis under rated design conditions With the data obtained previously, we will proceed to carry out the exergy analysis of the installation. To do this, the Exergy of each current will be calculated according to reference conditions, taking as a base an ambient temperature of 25ºC, as well as an ambient pressure of 1 atmosphere. It should be noted that the analysis will be carried out on each equipment of the installation with the exception of the degasser, condenser and superheater due to the following reasons respectively: • The capacitor is a device that discharges energy to the outside to convert the residual current into condensate, so when working with an open loop it is not possible to quantify how much exergy is destroyed and calculating the exergy efficiency is not useful. • On the other hand, exergy analysis is not carried out on the degasser because this equipment does not generate work or transform useful energy directly, but simply transfers heat to remove dissolved gases from the water, as mentioned above. Performing an exergy analysis would result in an efficiency higher than 100%, because this equipment recovers part of the energy from the steam used. This does not imply an increase in exergy, but a redistribution within the overall system. • As for the superheater, this equipment is essential but its importance in the system is not mainly due to an energy interest; the interest of the superheater lies in its capacity to raise the steam title in order to ensure that the current entering the low turbine has the lowest possible humidity. As its purpose is more mechanical than energetic, its analysis in the global exergy 25 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems impact of the installation will not be studied because it would give very low exergy efficiencies, as well as a considerably high destruction exergy, although it would certainly be an aspect to consider in a possible improvement of the installation. With these considerations made and the corresponding global exergy equation: 𝐸[𝐾𝐽 𝐾𝑔]=𝐸𝑓+𝐸𝑞+𝐸𝑝+𝐸𝑐 (27) This can be simplified by eliminating the potential and kinetic terms, as well as the term corresponding to a possible chemical reaction or transformation, which does not occur in any equipment, leaving a final equation to be applied in each stream: 𝐸𝑖[𝐾𝐽 𝐾𝑔]=𝐸𝑓= (𝑚 𝑚𝑑𝑜𝑡)∙((𝐻𝑖−ℎ𝑟𝑒𝑓)−𝑇0∙(𝑆𝑖−𝑠𝑟𝑒𝑓))(28) Where the exergy can be obtained in specific terms thanks to having defined all the enthalpy and exergy conditions in the previous energy analysis, as mentioned above, the starting conditions will be: 𝑇0[𝐾𝑒𝑙𝑣𝑖𝑛]=298,15 (29) 𝑃0[𝑏𝑎𝑟]=1,01325 (30) First, the corresponding exergy balance will be carried out for each equipment, where the value of the exergy destruction will be obtained, from which the exergy efficiency of each component will be calculated: ∑𝐸𝑥𝑒𝑟𝑔𝑦𝑓𝑢𝑒𝑙 𝑛 𝑖=1 =∑𝐸𝑥𝑒𝑟𝑔𝑦𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑛 𝑖=1 +𝐸𝑥𝑒𝑟𝑔𝑦𝑑𝑒𝑠𝑡𝑟𝑜𝑦𝑒𝑑+𝑊𝑖𝑛𝑡 (31) 𝜂𝑒𝑥𝑒𝑟𝑔𝑦𝑖[%]=(1−(𝐸𝑑𝑖) (∑𝐸𝑥𝑒𝑟𝑔𝑦𝑓𝑢𝑒𝑙 𝑛 𝑖=1 )∙100 (32) With this it is possible to extract the impact of each piece of equipment, in terms of percentage of exergy: Figure 13 Sankey's diagram of exergy destruction operating under rated design conditions Where it can be seen that the downstream turbine is responsible, in terms of exergy destruction, for almost half of the installation; the specific exergy destruction if the load were 100% takes a value of 79.14 KJ/kg. 4 ANALYSIS OF THE CYCLE UNDER VARIABLE LOAD OPERATION Once the analysis of the cycle has been completed, obtaining both the work and the required efficiencies, it is important to remember that the selected installation, an SMR, was chosen for its interest and capacity to operate at different load levels. Therefore, based on the results obtained in the previous sections, it is essential to analyse how the behaviour of the cycle varies when the load percentage is modified. 4.1 Equations and Considerations for part-load analysis To carry out the corresponding analysis, it will be necessary to define a series of variables and equations, which allow modifying the parameters of the base case, so it will begin by setting a maximum flow, and then a variable called "Load " will be defined that will be used to obtain the real flow with which it is operating, it will take values between 0.6 and 1, one being the operating situation in which it operates at maximum load. Load [−]=mdot mdotmax (33) 𝑚𝑑𝑜𝑡𝑚𝑎𝑥[𝑘𝑔 𝑠]=265,9 (34) Once defined, these two variables will be analysed as to how the variable load affects the main equipment, i.e. turbines and heat exchangers: 4.1.1 Turbines With regard to Turbines, using the Flügel equations [67], it is possible to analyse how the efficiency varies according to the percentage of work at which it is operated; these equations are identical for each turbine, the flow that enters the corresponding process will simply vary. When the effectiveness has changed, the new enthalpy of the turbine extractions will be calculated considering that the entropy is conserved in the process as before, but including the new efficiency; the rotation speeds will be considered constant as well as the compression ratio, i.e. the effect of the change in flow rate will be studied considering that the rest of the variables that have an influence do not change. With all this, the following equations will be added: 𝑛𝑒𝑑𝑜𝑡𝑖[−]=1 (𝑟𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑠𝑝𝑒𝑒𝑑) (35) 𝐺𝑒𝑖[𝑘𝑔 𝑠]=𝐿𝑜𝑎𝑑∗𝑚𝑑𝑜𝑡∙(1−∑𝛼i 𝑛 𝑖=1 )(36) 𝐺?𝑒𝑖[−]= 𝐺𝑒𝑖 (𝐺𝑒0𝑖)(37) 𝐺𝑒0𝑖[𝑘𝑔 𝑠]=𝑚𝑑𝑜𝑡∙(1−∑𝛼i 𝑛 𝑖=1 )(38) 𝜂𝑒𝑑𝑜𝑡𝑖[−]=𝜂𝑒𝑖 𝜂𝑒0 (39) 27 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems 𝜂𝑒0[−]=0,9 (40) 𝜂𝑒𝑑𝑜𝑡𝑖[−]= (1 − 𝑡4∙(1−𝑛𝑒𝑑𝑜𝑡𝑖)2)∙(𝑛𝑒𝑑𝑜𝑡𝑖 𝐺?𝑒𝑖 ) ∙ (2 − 𝑛𝑒𝑑𝑜𝑡𝑖 𝐺?𝑒𝑖 )(41) 𝑡4[−]=0,3 (42) Finally, it is possible to obtain the real efficiency depending on the load, which can be included as in the previous sections: 𝜂𝑒𝑖[−]=𝐻𝑖−𝐻𝑗 𝐻𝑖−𝐻𝑆𝑗 (43) 𝑊𝑒𝑡𝑢𝑟𝑏𝑖𝑛𝑒𝑛,𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖[𝐾𝐽 𝐾𝑔]=𝐻𝑖−𝐻𝑗 (44) 4.1.2 Heat Exchangers On the other hand, it will be necessary to calculate how the effectiveness of the heat exchangers varies, as well as their sizing and their impact on the system. For this purpose, the corresponding calculation equations [68] will be used; obtained from similar works where the operation of these is analysed in part-load operations; the equations will be defined for two generic currents, ‘i’ being the phase change current and ‘j’ the current to be heated, with temperatures l and k respectively. 𝜀 [−]=𝑄 𝑄𝑚𝑎𝑥 (45) 𝑄[𝐾𝑊]=𝐶𝑝𝑗∙𝑚𝑑𝑜𝑡𝑗 ∙ (𝑇[𝑘+1]−𝑇[𝑘]) (46) 𝑄𝑚𝑎𝑥[𝐾𝑊]=𝐶𝑚𝑖𝑛∙(𝑇[𝑙]−𝑇[𝑘]) (47) 𝐶𝑚𝑖𝑛=min((𝐶𝑝𝑗∙𝑚𝑑𝑜𝑡𝑗);(𝐶𝑝𝑖∙𝑚𝑑𝑜𝑡𝑖) ) (48) 𝑈[𝐾𝑊]=5 (49) 𝑅=0 {𝑃ℎ𝑎𝑠𝑒 𝑐ℎ𝑎𝑛𝑔𝑒}(50) 𝑁𝑇𝑈=𝑈∙𝐴 𝐶𝑚𝑖𝑛 (51) 𝜀[−]=1−𝑒(−𝑁𝑇𝑈) (52) Finally, the effectiveness obtained in each equipment is included in the equations corresponding to the calculation of alphan , where it is concluded that the main impact that resides in the variable load, as far as exchangers are concerned, is the flexibility as far as mass rate are concerned, that is to say, depending on the load percentage, these values will vary according to the needs of the cycle. 𝜀1∙(𝛼1∙(𝐻[9]−𝐻[8]))=(1−𝛼1−𝛼2−𝛼3)∙(𝐻[11]−𝐻[12]) (53) 𝜀2∙(𝛼2∙(𝐻[10]−𝐻[17]))=(1∙(𝐻[6]−𝐻[5]))(54) 𝜀3∙(𝛼4∙(𝐻[13]−𝐻[18]))=(1−𝛼1−𝛼2−𝛼3)∙(𝐻[3]−𝐻[2]) (55) 𝜀4∙(𝛼5∙(𝐻[14]−𝐻[19]))=(1−𝛼1−𝛼2−𝛼3)∙(𝐻[2]−𝐻[1]) (56) 𝜀5∙(𝛼3∙𝐻[11]+𝛼1∙𝐻[9]+𝛼2∙𝐻[17]+(1−𝛼1−𝛼2−𝛼3)∙𝐻[3])=1∙𝐻[4](57) Analysis of the cycle under variable load operation 28 28 4.1.3 Pump With regard to the behaviour of the pump under part-load conditions, it is observed that as the percentage of load decreases, so does its efficiency, which implies a slight increase in energy consumption. However, this consumption continues to be insignificant in the overall balance of the system. To estimate the efficiency under these conditions, an adjusted polynomial of pumps operating with similar flow rates and pressures under reduced loads has been calculated, which allows an accurate approximation of the real behaviour under different operating conditions. Figure 14 Variable load effect on pump performance 4.2 Analysis of performance and results obtained in different scenarios Once the cycle has been defined in its entirety, it will be necessary to carry out simulations to be able to see the response of the plant in the different scenarios when the load is varied. Thanks to the modelling programme itself, EES, it is possible to obtain numerical results by varying the load percentage in a very simple way, as mentioned above, this percentage has a range between 0.6 and 1. 4.2.1 Mass rate The impact that a load variation has on the installation affects not only the equipment itself, some values such as mass rate or fluid properties vary according to the percentage of load that is used. If an analysis of the respective mass rate is carried out, it is possible to see how at some points of the installation, such as the extraction that goes to the degasser (𝛼3) or the extraction corresponding to the bypass for reheating (𝛼1), they undergo significant changes, even though they have opposite tendencies; It can be seen that the lower the percentage of load, the lower the flow of steam diverted to the superheater, while in the extraction of the degasser, the lower the percentage of load, the higher the mass rate, this could be due to the need to improve the conditions of entry to the reactor, which, when working at a lower percentage of load, the thermodynamic conditions of the condensate entering are lower. On the other hand, the mass rate associated with the turbine extractions have very similar values to each other. The three extractions decrease slightly as the minimum load approaches; however, its range of variation is very 29 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems small. Figure 15 Variation of mass rate with load rate 4.2.2 Turbine With the above equations, a substantial variation in the efficiency of the turbines can be foreseen, as well as a notable variation in the work provided by the turbines. The efficiency of the turbines is the same for all the turbines, due to the fact that, by varying with the percentage of load, they all undergo the same changes in their operation. Looking first at efficiency: Figure 16 Turbine efficiency variation with load rate It is possible to observe how the efficiency of the turbine follows a curve that is accentuated in the values close to the minimum load stipulated, this efficiency indicates as could be expected that a decrease in the load in addition to leading to changes in the work, causes a decrease in the efficiency, since the turbines chosen are designed, as well as the installation, to work under conditions of maximum power; This decrease in efficiency gives rise to changes in the thermodynamic properties of the currents that, on passing through each extraction, undergo notable changes. This variation is verified using Flügel's equations (35-44), where efficiency decreases as load varies. Analysis of the cycle under variable load operation 30 30 These changes, for example, are reflected in properties such as enthalpy that affect the work obtained: Figure 17 Variation specific work turbines with load rate As can be seen, the most important extractions, in terms of work produced, suffer greater changes generated by the load, as in the case of the last extraction of the low turbine, or the first extraction of the high turbine, which suffer changes of around 150 KW/Kg when we vary the load; the rest of the extractions, as they have less impact on the work produced, do not suffer such notable changes. Undoubtedly, the variation of the thermodynamic properties of the fluid causes an important change in the performance of the turbines. Where, as the efficiency and thermodynamic properties of the flows have changed, the specific work of each flow decreases, as can be seen in equation (6). In terms of absolute work, combining the extractions with the respective turbines, the evolution of the power produced follows a similar evolution as a function of the load, where it can be observed that at reduced load values the work produced by the turbines approaches and they start to have a similar power production. Figure 18 Total work output of the turbines vs. Load rate 31 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems 4.2.3 Reactor analysis The enthalpy of the fuel and product of the reactor are fixed, which is why when the load varies the conditions and properties of the cycle change to adapt to the needs of the reactor, for this reason, the specific work, unlike equipment such as turbines, does not vary because they do not suffer changes in the specific enthalpies of input and output, so as you can see the heat that is necessary to provide the reactor varies linearly with the percentage of load. This makes sense in relation to what we saw earlier in equation (7), where we observed that the enthalpy jump remains constant and therefore the total heat of the reactor depends linearly on the steam load rate. Figure 19 Variation of heat required in the reactor with load rate 4.2.4 Overall efficiency With regard to the overall efficiency of the installation, this reaches its maximum value at nominal load conditions. It is possible to highlight how, from values close to 80% load, the slope of the efficiency curve begins to increase significantly, with an acceleration in the loss of efficiency being observed. This trend becomes more pronounced at around 60% load, at which point the efficiency drops considerably to approximately half its initial value. This behaviour confirms the initial hypothesis of a safe operating range between 0.6 and 1.0 of the nominal load, as operating below this range would imply marked efficiency losses. Analysis of the cycle under variable load operation 32 32 Figure 20 Efficiency variation of the SMR nuclear power plant under different load rates. 5 OFF-DESIGN SMR EXERGY ANALYSIS Once the study of the functioning of the equipment operating at part-load and how this affects their respective operating ranges, as well as their performance, the next step will be an exergy analysis both globally and by elements of the installation. 5.1 Variable load SMR exergy analysis As has been analyzed and demonstrated in the previous points, working at different load values significantly affects the thermodynamic conditions of the currents, as well as the yields and efficiencies of certain equipment that cause notable changes in the exergy study. That is why we will proceed to comment on the different scenarios and their effects: 5.1.1 Exergy destruction low-pressure turbine The low-pressure turbine of the installation is made up of three extractions, among which we find the residual extraction where there is the jump with the greatest enthalpy difference; therefore, when the load varies, the exergy increases considerably, which is why the equipment, in terms of exergy, is not able to work correctly, penalising considerably both the work and the exergy destruction, it is the element of the installation that suffers most from these variations. Figure 21 Specific exergy destruction low-pressure turbine as a function of load rate As can be seen, when working close to the minimum load value, the specific exergy is accentuated; the graph indicates that despite the increase of the exergy values when working at low load values, its exergy performance works in an acceptable way in a range of [0.8-1], once this range is passed, the losses increase and can affect in a very negative way the global losses. In conjunction with this idea, it can be seen that in the percentage of total exergy destruction, the contribution of Off-design smr exergy analysis 40 40 5.3 Exergy analysis of operation pressure Next, an analysis of the performance of the exergy destruction will be carried out as a function of the pressure of the turbine extractions, allowing us to identify their performance and operation by varying their values. There are five extraction pressures, two in the high turbine and three in the low turbine, which will undergo significant changes when varying these pressure values; on the other hand, the extractions that are subsequently used in the preheating also affect the heat exchangers, which is why they will be analysed as a function of the corresponding extraction pressure. 5.3.1 Low-pressure turbine The first element of the installation to be analysed is the low-pressure turbine. This equipment, as mentioned above, has three extractions and is the element that produces the most work, which is why the value of the corresponding pressures must be optimised whenever possible, seeking a balance between the work produced and both the energy and exergy efficiency of the components. If we analyse the first extraction, which had the value of the corresponding pressure at 3.5 bar, we can see that if the pressure value is varied, the specific exergy destruction does not undergo major changes, as we mentioned, this is due to the fact that the first extraction involves a smaller enthalpic jump, something that also happens in the high pressure turbine, which is why in choosing the appropriate value of the pressure of the low pressure turbine, the exergy aspect takes on a secondary role due to its small variation. Figure 33 Specific exergy destruction low-pressure turbine as a function of P [13] On the other hand, it can be seen that the second extraction reproduces an analogous situation, where a variation in the product pressure does not notably affect the exergy destruction, so that, like the first extraction, the choice 41 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems of this value does not involve an exergy improvement, as its influence is reduced. Figure 34 Specific exergy destruction low turbine as a function of P [14] Finally, it can be seen how, in the residual extraction, the value chosen for the product pressure plays a fundamental role in the total amount of exergy destruction in the low pressure turbine. It can be observed that the higher the value of P[15], the exergy destruction decreases considerably, which is why in the choice of the residual extraction pressure, a lower pressure considerably improves the losses of the equipment, which implies a better overall exergy efficiency and lower losses, while the work produced will be lower. Figure 35 Specific exergy destruction low-pressure turbine as a function of P [15] 5.3.2 High-pressure turbine As for the high-pressure turbine, the two pressures that affect its operation are the pressure of the first extraction (P[10]) which is later used in the preheater prior to the reactor, and the pressure of the second extraction (P[11]), which will later be used in the low-level turbine. If the first extraction is analyzed, it can be observed that despite significantly varying the pressure, in a range of 4 bars, the destruction exergy hardly varies, which is why when seeing this effect, it can be concluded that by not having a significant impact on the exergy, it could be possible to reduce the pressure of the extraction to obtain more work; The value of this pressure is in turn limited by the steam titer, which if it decreases considerably can affect the operation of preheater 3 that would imply losses, so the value would have to be optimized so that it was the minimum possible compatible with the rest of the cycle Off-design smr exergy analysis 42 42 Figure 36 Specific exergy destruction high-pressure turbine as a function of P [10] On the other hand, if an analogous analysis of the destruction exergy is carried out as a function of the pressure of the second extraction, it can be seen that when imposing the pressure in a smaller range, the exergy destruction varies in a more accentuated way, this is due to the greater enthalpic jump existing in the second extraction. It is important to add how the value of pressure 11 is limited by the maximum pressure allowed by the cycle, since if it were to increase it could take values very similar to the previous extraction, reducing the work provided and with it the performance of the turbine. Figure 37 Specific exergy destruction high-pressure turbine as a function of P [11] 5.3.3 Preheater 1 On the other hand, it can be seen how preheater 1, which is the first to contribute heat to the condensate stream, is clearly influenced by the exergy losses generated by the choice of pressure [14], the graph shows how at low pressures of the corresponding extraction the exergy destruction decreases considerably, despite this, the lower the pressure, the lower the energy contributed to the stream to be preheated and this can lead to global malfunctions as there is no effective exchange; For this reason, it is necessary to reach a balance between the minimum losses without affecting the efficiency of the cycle, which can be reduced by a bad preheating. 43 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems . Figure 38 Specific exergy destruction preheater 1 as a function of P[14] 5.3.4 Preheater 2 If a similar analysis is carried out for the second preheater, in which the extraction pressure of low-pressure [13], takes an important value in the variation of the destruction exergy of preheater 2, it is the second equipment in the preheating chain and is the element prior to the degasser; If you look at the graph, you can analyze an evolution similar to that seen in preheater 1. Figure 39 Specific exergy destruction preheater 2 as a function of P[13] Despite this observation, the function that follows the graph is practically linear, as well as lower values of exergy destruction, so that, although working at low pressures could decrease the value of the exergy destruction, its weight in percentage terms of exergy destruction of the installation is lower than other elements. 5.3.5 Preheater 3 Finally, preheater 3 also has a linear function, as does preheater 2; the unit to be studied is the preheater before Off-design smr exergy analysis 44 44 the reactor and the extraction pressure that affects its operation is P [10]; as we can see, despite being greater than that of preheater 2 in energy terms, it is lower than that of preheater 1, despite there being a wide range in the vapour pressure. Figure 40 Specific exergy destruction preheater 3 as a function of P[10] 5.4 Variation of thermodynamic parameters of the steam cycle The operation of the cycle is defined by certain parameters which can be modified in the search for an optimisation or possible improvement of the thermodynamic cycle; these parameters have been selected in the base case on the basis of other works and other installations with typical parameters; nevertheless, it is advisable to analyse, within a coherent working range, how these parameters affect the thermodynamic cycle as well as the installation from an exergy point of view. 5.4.1 Inlet turbine Pressure The variation of this parameter will be set by the safety range discussed for the correct operation of SMR reactors, which is specifically (13.96-17.06) bar [61], First, before analyzing the exergy impact it has on the equipment, as well as on the installation, an overview of how fundamental operating parameters vary will be made. If the work produced by the turbines is analyzed, it can be seen that the low-pressure turbine, which generates most of the work, does not undergo great changes when the inlet turbine pressure is varied, it can be seen how the trend is decreasing but in a reduced interval. On the other hand, the work produced by the high turbine is more influenced by the pressure chosen, where it can be seen how it has a decreasing tendency to higher values of vapor pressure, despite this, the variation in both specific works is small. That is why a lower live vapour pressure would be of interest in the choice since it implies a greater specific work produced. 45 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems Figure 41 Variation of work produced as a function of the inlet turbine pressure On the other hand, if the overall efficiency is analysed, it can be seen that in general terms it does not have a significant impact due to the fact that between the minimum and maximum value of inlet turbine pressure, an increase of 0.20% in efficiency is achieved. It should be added that this improvement in efficiency is also due to a greater work produced, which reinforces the idea commented previously, that a lower operating pressure in the reactor leads to multiple improvements in terms of operation. Figure 42 Variation of overall plant efficiency as a function of the inlet turbine pressure If we now analyse the exergy impact it has, we can see that its impact is again very small. It is worth noting that the high-pressure turbine destroys more exergy at lower inlet turbine pressure, and therefore has a worse exergy efficiency, while the low-pressure turbine remains practically constant. Finally, if we analyse the exergies destruction by the exchangers, we can see that they hardly suffer any exergy variation, so they are not equipment Off-design smr exergy analysis 46 46 that are affected by changes in the reactor steam pressure. Figure 42 Exergy variation destruction by elements as a function of inlet turbine pressure 5.4.2 Live Steam Temperature As previously mentioned with the live vapor pressure, the temperature selected for the base case was justified by selecting the highest possible within the corresponding safety interval, which is (511.2-624.8) Kelvin, which is why it will be analyzed first how this choice of temperature influences the general performance and then its exergy analysis. In this way, a global study can be carried out, taking into account all the aspects that are affected. In the first place, if we analyze the work produced by the installation according to the temperature of live steam, we observe that there is a value, for which the high-pressure turbine produces a greater power, on the other hand, if the situation of the low-pressure turbine is analyzed, it is possible to observe how it has a decreasing trend with the increase in temperature. Figure 43 Variation of work produced as a function of the live steam temperature For this reason, it is necessary to make a new graph in which the impact of the live steam temperature on the total work produced can be correctly analyzed; This graph shows how the maximum work produced is produced 47 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems with a live steam temperature value of 571.5 Kelvin, from this temperature the work produced is considerably reduced, showing a possible optimization of the installation with which more work could be obtained. Figure 44 Variation of total produced work as a function of the live steam temperature On the other hand, it can be observed that as the temperature increases from 500 kelvin, the efficiency also increases, reaching a maximum value of around 33.3 % at around 600 kelvin; after this point, it can be observed that the efficiency decreases due to the decrease in the work produced as well as the possible increase in losses. Figure 45 Variation in the overall efficiency of the installation as a function of the live steam temperature Finally, it can be observed how the destruction exergy of the turbines follows an evolution similar to the work produced in them, where the greater the work, the greater the exergy losses, on the other hand, it is observed that the higher the temperature of live steam, the losses corresponding to preheater 1, decrease, unlike preheaters 2 and 3 whose exergy remains constant Off-design smr exergy analysis 48 48 Figure 46 Exergy variation destruction by elements as a function of live steam temperature 5.5 Conclusions and discussions This section presents the conclusions of the exergy analysis carried out under two different operating conditions: at part-load (0.6) and at full load (1). The comparison between these two scenarios studied in the previous sections allows us to evaluate the impact that the load variation has on the exergy performance of the system. Figure 47 Exergy efficiencies as a function of load rate A comparison is made of the exergy efficiency of each element studied, it can be seen how the low-pressure turbine, which, as we have seen above, is the equipment that destroys the most exergy, despite having an acceptable efficiency of 93% under design conditions, when operating at minimum load values, its efficiency drops to 68%. It is the element of the installation that destroys the most exergy, and such a marked variation in its efficiency is mainly due to the fact that, as it works with steam at lower pressure and temperature conditions, it is particularly sensitive to the reduction in steam flow under part-load conditions, which produces a less efficient expansion and a relative increase in irreversible losses. In addition, as it moves away from the optimal 49 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems design point, the utilisation of the pressure drop is limited, which significantly reduces the useful work it can generate and thus its exergy efficiency. On the other hand, the high pressure turbine follows a similar graph but with a lower slope when it starts to decay, this is due to the fact that as it generates less work these losses are less accentuated, in spite of this the graph is similar due to the fact that the mentioned losses are caused by the same reasons, less efficient expansions, as well as steam currents operating in worse conditions and temperatures; All this causes the efficiency to go from 96% to 83.3%, a minor variation but in any case notable. If we analyse the exergy performance of the exchangers, their performance decreases but follows a smoother evolution, varying in the order of 7% in preheater 1, due to being the preheater that operates with condensate water at lower temperatures and the preheater where the temperature jump is greater between the two streams, this effect increases at part-load where the condensate outlet temperature is lower and there is a greater exergy destruction. On the other hand, preheater 2 and preheater 3 suffer similar losses of around 4% and 2% respectively, an evolution that could be predicted by looking at the effect on the values of exergy destruction in the previous sections. If the Sankey diagrams of the different situations are compared again and simultaneously, it can be seen how the exergy losses are mainly concentrated in the turbines, i.e. it can be seen how operating under off-design conditions causes a more accentuated loss in these elements, which are the ones that have the greatest overall weight in the installation. Figure 48 Distribution of Exergy for Loads of 1 and 0,6 Below, if the following two graphs are analyzed, it can be seen how this percentage impact of exergy by equipment takes value in each component, as well as in the overall installation Figure 49 Specific exergy destruction variation by component and total with system load SMR exergy optimization 56 56 It can be seen how a lower extraction pressure allows the installation to increase its enthalpy jump and therefore, as the extraction produces more work, the power of the installation increases considerably. On the other hand, at a lower extraction pressure, the losses increase considerably, causing a worse performance from the energy point of view and decreasing the efficiency of the equipment. This is why, if we analyse the evolution of the graph, in this work we have opted for an optimisation at an intermediate point, i.e. the extraction pressure will be set at 0.4 bar, in such a way that the losses are reduced so as not to reach the most unfavourable situation; this decision is based on finding a situation of equilibrium between both effects. In any case, this study shows how, depending on the use and the chosen criteria, one effect or the other can be chosen. Once this improvement has been implemented, the changes produced in the cycle can be observed: Figure 59 Analysis of exergy improvements complementary optimization Where losses have been reduced by 22.36% operating under rated design conditions, as well as an improvement of 21.16% operating at minimum load values, considerably greater improvements with respect to the base case analysed previously. Figure 60 Analysis of improvements to complementary power optimization If we analyse the effect of the exergy optimisation on the performance of the turbines, we can see that for the rated design conditions, the workload decreases by 10.13%, while operating under minimum load conditions we can see that the workload has decreased by 9.94%, in both situations the performance of the system has decreased, but in a more gentle way with respect to the exergy improvement, where improvement percentages of more than double are reached. 57 Operational Analysis of Small Modular Reactor Plants Integrated into Distributed Energy Systems On the other hand, the efficiency has decreased due to a loss of power; if this optimisation is carried out, the efficiency in rated design conditions decreases to a value of 29.14%, which is why the decision to implement this possible improvement lies in the interest of one improvement or the other. 6.4 Conclusion As has been demonstrated, the designed installation meets the specified requirements. This system is capable of reducing the environmental impact—specifically in terms of greenhouse gas emissions—associated with conventional power generation methods such as coal or natural gas. Furthermore, it ensures a constant and stable power output, guaranteeing electricity supply in areas where access to the grid is limited or non-existent. Additionally, it offers significant adaptability by being able to operate under varying load conditions. Although it is a Small Modular Reactor (SMR), its overall performance is comparable to that of a large-scale nuclear power plant. This highlights the effectiveness of the selected cycle in terms of efficiency when compared with other installations utilizing similar technologies. Regarding the power output, both under the initial conditions and in the two proposed optimizations, the cycle is capable of delivering the required and designspecified power. Moreover, it can adapt to different load percentages, allowing the installation to operate efficiently at various levels of demand. As a final consideration on this aspect, it would be advisable to conduct a more detailed study to determine the optimal minimum load at which the installation should operate, since performance drops significantly at load values around 0.6. From an exergy standpoint, it has been observed that at lower load values, the exergy efficiency decreases while the exergy destruction in each component increases. This reveals that, despite being a promising system due to its operational versatility, the performance in terms of exergy degrades at reduced loads, leading to a lower net energy benefit. Moreover, this installation falls within the category of distributed generation, which represents a clear advantage over traditional centralized systems. Being closer to the point of consumption reduces transmission losses and enhances overall efficiency. In a context of growing energy demand—driven by increasing industrial activity— such solutions become increasingly necessary and attractive for deployment. Its ability to adapt to different load levels and ease of integration into local grids, operating in a complementary manner, enables not only the coverage of current demand but also an efficient response to potential changes in consumer behavior and societal needs. In conclusion, SMR technology represents a realistic, efficient, and sustainable alternative to conventional power generation models. Its capability to be integrated into hybrid and decentralized systems enhances energy security and facilitates the transition toward a cleaner energy model. It has been shown that this particular installation demonstrates that SMRs can match the performance of large nuclear power plants while maintaining high operational flexibility. 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