@inproceedings{SattlerAlexopoulosCaminosetal.2019, author = {Sattler, Johannes, Christoph and Alexopoulos, Spiros and Caminos, Ricardo Alexander Chico and Mitchell, John C. and Ruiz, Victor C. and Kalogirou, Soteris and Ktistis, Panayiotis K. and Teixeira Boura, Cristiano Jos{\´e} and Herrmann, Ulf}, title = {Dynamic simulation model of a parabolic trough collector system with concrete thermal energy storage for process steam generation}, series = {AIP Conference Proceedings}, volume = {2126}, booktitle = {AIP Conference Proceedings}, issn = {0094243X}, doi = {10.1063/1.5117663}, pages = {150007-1 -- 150007-8}, year = {2019}, language = {en} } @article{WoliszSchuetzBlankeetal.2017, author = {Wolisz, Henryk and Sch{\"u}tz, Thomas and Blanke, Tobias and Hagenkamp, Markus and Kohrn, Markus and Wesseling, Mark and M{\"u}ller, Dirk}, title = {Cost optimal sizing of smart buildings' energy system components considering changing end-consumer electricity markets}, series = {Energy}, volume = {137}, journal = {Energy}, publisher = {Elsevier}, address = {Amsterdam}, doi = {10.1016/j.energy.2017.06.025}, pages = {715 -- 728}, year = {2017}, language = {en} } @inproceedings{BlankeDringVonteinetal.2018, author = {Blanke, Tobias and Dring, Bernd and Vontein, Marius and Kuhnhenne, Markus}, title = {Climate Change Mitigation Potentials of Vertical Building Integrated Photovoltaic}, series = {8th International Workshop on Integration of Solar Power into Power Systems : 16-17 October 2018, Stockholm, Sweden}, booktitle = {8th International Workshop on Integration of Solar Power into Power Systems : 16-17 October 2018, Stockholm, Sweden}, pages = {1 -- 7}, year = {2018}, language = {en} } @inproceedings{KreyerMuellerEsch2020, author = {Kreyer, J{\"o}rg and M{\"u}ller, Marvin and Esch, Thomas}, title = {A Map-Based Model for the Determination of Fuel Consumption for Internal Combustion Engines as a Function of Flight Altitude}, publisher = {DGLR}, address = {Bonn}, doi = {10.25967/490162}, pages = {13 Seiten}, year = {2020}, abstract = {In addition to very high safety and reliability requirements, the design of internal combustion engines (ICE) in aviation focuses on economic efficiency. The objective must be to design the aircraft powertrain optimized for a specific flight mission with respect to fuel consumption and specific engine power. Against this background, expert tools provide valuable decision-making assistance for the customer. In this paper, a mathematical calculation model for the fuel consumption of aircraft ICE is presented. This model enables the derivation of fuel consumption maps for different engine configurations. Depending on the flight conditions and based on these maps, the current and the integrated fuel consumption for freely definable flight emissions is calculated. For that purpose, an interpolation method is used, that has been optimized for accuracy and calculation time. The mission boundary conditions flight altitude and power requirement of the ICE form the basis for this calculation. The mathematical fuel consumption model is embedded in a parent program. This parent program presents the simulated fuel consumption by means of an example flight mission for a representative airplane. The focus of the work is therefore on reproducing exact consumption data for flight operations. By use of the empirical approaches according to Gagg-Farrar [1] the power and fuel consumption as a function of the flight altitude are determined. To substantiate this approaches, a 1-D ICE model based on the multi-physical simulation tool GT-Suite® has been created. This 1-D engine model offers the possibility to analyze the filling and gas change processes, the internal combustion as well as heat and friction losses for an ICE under altitude environmental conditions. Performance measurements on a dynamometer at sea level for a naturally aspirated ICE with a displacement of 1211 ccm used in an aviation aircraft has been done to validate the 1-D ICE model. To check the plausibility of the empirical approaches with respect to the fuel consumption and performance adjustment for the flight altitude an analysis of the ICE efficiency chain of the 1-D engine model is done. In addition, a comparison of literature and manufacturer data with the simulation results is presented.}, language = {en} } @incollection{HoffschmidtAlexopoulosRauetal.2022, author = {Hoffschmidt, Bernhard and Alexopoulos, Spiros and Rau, Christoph and Sattler, Johannes, Christoph and Anthrakidis, Anette and Teixeira Boura, Cristiano Jos{\´e} and O'Connor, B. and Chico Caminos, R.A. and Rend{\´o}n, C. and Hilger, P.}, title = {Concentrating solar power}, series = {Comprehensive Renewable Energy (Second Edition) / Volume 3: Solar Thermal Systems: Components and Applications}, booktitle = {Comprehensive Renewable Energy (Second Edition) / Volume 3: Solar Thermal Systems: Components and Applications}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-0-12-819734-9}, pages = {670 -- 724}, year = {2022}, abstract = {The focus of this chapter is the production of power and the use of the heat produced from concentrated solar thermal power (CSP) systems. The chapter starts with the general theoretical principles of concentrating systems including the description of the concentration ratio, the energy and mass balance. The power conversion systems is the main part where solar-only operation and the increase in operational hours. Solar-only operation include the use of steam turbines, gas turbines, organic Rankine cycles and solar dishes. The operational hours can be increased with hybridization and with storage. Another important topic is the cogeneration where solar cooling, desalination and of heat usage is described. Many examples of commercial CSP power plants as well as research facilities from the past as well as current installed and in operation are described in detail. The chapter closes with economic and environmental aspects and with the future potential of the development of CSP around the world.}, language = {en} } @incollection{HoffschmidtAlexopoulosGoettscheetal.2022, author = {Hoffschmidt, Bernhard and Alexopoulos, Spiros and G{\"o}ttsche, Joachim and Sauerborn, Markus and Kaufhold, O.}, title = {High Concentration Solar Collectors}, series = {Comprehensive Renewable Energy (Second Edition) / Volume 3: Solar Thermal Systems: Components and Applications}, booktitle = {Comprehensive Renewable Energy (Second Edition) / Volume 3: Solar Thermal Systems: Components and Applications}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-0-12-819734-9}, doi = {10.1016/B978-0-12-819727-1.00058-3}, pages = {198 -- 245}, year = {2022}, abstract = {Solar thermal concentrated power is an emerging technology that provides clean electricity for the growing energy market. To the solar thermal concentrated power plant systems belong the parabolic trough, the Fresnel collector, the solar dish, and the central receiver system. For high-concentration solar collector systems, optical and thermal analysis is essential. There exist a number of measurement techniques and systems for the optical and thermal characterization of the efficiency of solar thermal concentrated systems. For each system, structure, components, and specific characteristics types are described. The chapter presents additionally an outline for the calculation of system performance and operation and maintenance topics. One main focus is set to the models of components and their construction details as well as different types on the market. In the later part of this article, different criteria for the choice of technology are analyzed in detail.}, language = {en} } @inproceedings{SchwagerTeixeiraBouraFleschetal.2019, author = {Schwager, Christian and Teixeira Boura, Cristiano Jos{\´e} and Flesch, Robert and Alexopoulos, Spiros and Herrmann, Ulf}, title = {Improved efficiency prediction of a molten salt receiver based on dynamic cloud passage simulation}, series = {AIP Conference Proceedings}, volume = {2126}, booktitle = {AIP Conference Proceedings}, number = {1}, isbn = {978-0-7354-1866-0}, doi = {10.1063/1.5117566}, pages = {030054-1 -- 030054-8}, year = {2019}, language = {en} } @inproceedings{GorzalkaDahlkeGoettscheetal.2018, author = {Gorzalka, Philip and Dahlke, Dennis and G{\"o}ttsche, Joachim and Israel, Martin and Patel, Dhruvkumar and Prahl, Christoph and Schmiedt, Jacob Estevam and Frommholz, Dirk and Hoffschmidt, Bernhard and Linkiewicz, Magdalena}, title = {Building Tomograph-From Remote Sensing Data of Existing Buildings to Building Energy Simulation Input}, series = {EBC, Annex 71, Fifth expert meeting, October 17-19, 2018, Innsbruck, Austria}, booktitle = {EBC, Annex 71, Fifth expert meeting, October 17-19, 2018, Innsbruck, Austria}, pages = {17 Seiten}, year = {2018}, language = {en} } @article{SattlerRoegerSchwarzboezletal.2020, author = {Sattler, Johannes, Christoph and R{\"o}ger, Marc and Schwarzb{\"o}zl, Peter and Buck, Reiner and Macke, Ansgar and Raeder, Christian and G{\"o}ttsche, Joachim}, title = {Review of heliostat calibration and tracking control methods}, series = {Solar Energy}, volume = {207}, journal = {Solar Energy}, publisher = {Elsevier}, address = {Amsterdam}, doi = {10.1016/j.solener.2020.06.030}, pages = {110 -- 132}, year = {2020}, abstract = {Large scale central receiver systems typically deploy between thousands to more than a hundred thousand heliostats. During solar operation, each heliostat is aligned individually in such a way that the overall surface normal bisects the angle between the sun's position and the aim point coordinate on the receiver. Due to various tracking error sources, achieving accurate alignment ≤1 mrad for all the heliostats with respect to the aim points on the receiver without a calibration system can be regarded as unrealistic. Therefore, a calibration system is necessary not only to improve the aiming accuracy for achieving desired flux distributions but also to reduce or eliminate spillage. An overview of current larger-scale central receiver systems (CRS), tracking error sources and the basic requirements of an ideal calibration system is presented. Leading up to the main topic, a description of general and specific terms on the topics heliostat calibration and tracking control clarifies the terminology used in this work. Various figures illustrate the signal flows along various typical components as well as the corresponding monitoring or measuring devices that indicate or measure along the signal (or effect) chain. The numerous calibration systems are described in detail and classified in groups. Two tables allow the juxtaposition of the calibration methods for a better comparison. In an assessment, the advantages and disadvantages of individual calibration methods are presented.}, language = {en} } @article{ElMoussaouiTalbiAtmaneetal.2020, author = {El Moussaoui, Noureddine and Talbi, Sofian and Atmane, Ilyas and Kassmi, Khalil and Schwarzer, Klemens and Chayeb, Hamid and Bachiri, Najib}, title = {Feasibility of a new design of a Parabolic Trough Solar Thermal Cooker (PSTC)}, series = {Solar Energy}, volume = {201}, journal = {Solar Energy}, number = {Vol. 201 (May 2020)}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0038-092X}, doi = {10.1016/j.solener.2020.03.079}, pages = {866 -- 871}, year = {2020}, abstract = {In this article, we describe the structure, the functioning, and the tests of parabolic trough solar thermal cooker (PSTC). This oven is designed to meet the needs of rural residents, including Urban, which requires stable cooking temperatures above 200 °C. The cooking by this cooker is based on the concentration of the sun's rays on a glass vacuum tube and heating of the oil circulate in a big tube, located inside the glass tube. Through two small tubes, associated with large tube, the heated oil, rise and heats the pot of cooking pot containing the food to be cooked (capacity of 5 kg). This cooker is designed in Germany and extensively tested in Morocco for use by the inhabitants who use wood from forests. During a sunny day, having a maximum solar radiation around 720 W/m2 and temperature ambient around 26 °C, maximum temperatures recorded of the small tube, the large tube and the center of the pot are respectively: 370 °C, 270 °C and 260 °C. The cooking process with food at high (fries, ..), we show that the cooking oil temperature rises to 200 °C, after 1 h of heating, the cooking is done at a temperature of 120 °C for 20 min. These temperatures are practically stable following variations and decreases in the intensity of irradiance during the day. The comparison of these results with those of the literature shows an improvement of 30-50 \% on the maximum value of the temperature with a heat storage that could reach 60 min of autonomy. All the results obtained show the good functioning of the PSTC and the feasibility of cooking food at high temperature (>200 °C).}, language = {en} } @incollection{HoffschmidtAlexopoulosRauetal.2021, author = {Hoffschmidt, Bernhard and Alexopoulos, Spiros and Rau, Christoph and Sattler, Johannes, Christoph and Anthrakidis, Anette and Teixeira Boura, Cristiano Jos{\´e} and O'Connor, B. and Caminos, R.A. Chico and Rend{\´o}n, C. and Hilger, P.}, title = {Concentrating Solar Power}, series = {Earth systems and environmental sciences}, booktitle = {Earth systems and environmental sciences}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-0-12-409548-9}, doi = {10.1016/B978-0-12-819727-1.00089-3}, year = {2021}, abstract = {The focus of this chapter is the production of power and the use of the heat produced from concentrated solar thermal power (CSP) systems. The chapter starts with the general theoretical principles of concentrating systems including the description of the concentration ratio, the energy and mass balance. The power conversion systems is the main part where solar-only operation and the increase in operational hours. Solar-only operation include the use of steam turbines, gas turbines, organic Rankine cycles and solar dishes. The operational hours can be increased with hybridization and with storage. Another important topic is the cogeneration where solar cooling, desalination and of heat usage is described. Many examples of commercial CSP power plants as well as research facilities from the past as well as current installed and in operation are described in detail. The chapter closes with economic and environmental aspects and with the future potential of the development of CSP around the world.}, language = {en} } @article{DammSauerbornFendetal.2017, author = {Damm, Marc Andr{\´e} and Sauerborn, Markus and Fend, Thomas and Herrmann, Ulf}, title = {Optimisation of a urea selective catalytic reduction system with a coated ceramic mixing element}, series = {Journal of ceramic science and technology}, volume = {8}, journal = {Journal of ceramic science and technology}, number = {1}, publisher = {G{\"o}ller}, address = {Baden-Baden}, isbn = {2190-9385 (Print)}, issn = {2190-9385 (Online)}, doi = {10.4416/JCST2016-00056}, pages = {19 -- 24}, year = {2017}, language = {en} } @article{AlexopoulosHoffschmidt2017, author = {Alexopoulos, Spiros and Hoffschmidt, Bernhard}, title = {Advances in solar tower technology}, series = {Wiley interdisciplinary reviews : Energy and Environment : WIREs}, volume = {6}, journal = {Wiley interdisciplinary reviews : Energy and Environment : WIREs}, number = {1}, publisher = {Wiley}, address = {Weinheim}, issn = {2041-840X}, doi = {10.1002/wene.217}, pages = {1 -- 19}, year = {2017}, language = {en} } @inproceedings{ElMoussaouiKassmiAlexopoulosetal.2021, author = {El Moussaoui, Noureddine and Kassmi, Khalil and Alexopoulos, Spiros and Schwarzer, Klemens and Chayeb, Hamid and Bachiri, Najib}, title = {Simulation studies on a new innovative design of a hybrid solar distiller MSDH alimented with a thermal and photovoltaic energy}, series = {Materialstoday: Proceedings}, volume = {45}, booktitle = {Materialstoday: Proceedings}, number = {8}, publisher = {Elsevier}, address = {Amsterdam}, issn = {2214-7853}, doi = {10.1016/j.matpr.2021.03.115}, pages = {7653 -- 7660}, year = {2021}, abstract = {In this paper, we present the structure, the simulation the operation of a multi-stage, hybrid solar desalination system (MSDH), powered by thermal and photovoltaic (PV) (MSDH) energy. The MSDH system consists of a lower basin, eight horizontal stages, a field of four flat thermal collectors with a total area of 8.4 m2, 3 Kw PV panels and solar batteries. During the day the system is heated by thermal energy, and at night by heating resistors, powered by solar batteries. These batteries are charged by the photovoltaic panels during the day. More specifically, during the day and at night, we analyse the temperature of the stages and the production of distilled water according to the solar irradiation intensity and the electric heating power, supplied by the solar batteries. The simulations were carried out in the meteorological conditions of the winter month (February 2020), presenting intensities of irradiance and ambient temperature reaching 824 W/m2 and 23 °C respectively. The results obtained show that during the day the system is heated by the thermal collectors, the temperature of the stages and the quantity of water produced reach 80 °C and 30 Kg respectively. At night, from 6p.m. the system is heated by the electric energy stored in the batteries, the temperature of the stages and the quantity of water produced reach respectively 90 °C and 104 Kg for an electric heating power of 2 Kw. Moreover, when the electric power varies from 1 Kw to 3 Kw the quantity of water produced varies from 92 Kg to 134 Kg. The analysis of these results and their comparison with conventional solar thermal desalination systems shows a clear improvement both in the heating of the stages, by 10\%, and in the quantity of water produced by a factor of 3.}, language = {en} } @inproceedings{SattlerCaminosUerlingsetal.2020, author = {Sattler, Johannes, Christoph and Caminos, Ricardo Alexander Chico and {\"U}rlings, Nicolas and Dutta, Siddharth and Ruiz, Victor and Kalogirou, Soteris and Ktistis, Panayiotis and Agathokleous, Rafaela and Jung, Christian and Alexopoulos, Spiros and Atti, Vikrama Nagababu and Teixeira Boura, Cristiano Jos{\´e} and Herrmann, Ulf}, title = {Operational experience and behaviour of a parabolic trough collector system with concrete thermal energy storage for process steam generation in Cyprus}, series = {AIP Conference Proceedings}, booktitle = {AIP Conference Proceedings}, number = {2303}, doi = {10.1063/5.0029278}, pages = {140004-1 -- 140004-10}, year = {2020}, abstract = {As part of the transnational research project EDITOR, a parabolic trough collector system (PTC) with concrete thermal energy storage (C-TES) was installed and commissioned in Limassol, Cyprus. The system is located on the premises of the beverage manufacturer KEAN Soft Drinks Ltd. and its function is to supply process steam for the factory's pasteurisation process [1]. Depending on the factory's seasonally varying capacity for beverage production, the solar system delivers between 5 and 25 \% of the total steam demand. In combination with the C-TES, the solar plant can supply process steam on demand before sunrise or after sunset. Furthermore, the C-TES compensates the PTC during the day in fluctuating weather conditions. The parabolic trough collector as well as the control and oil handling unit is designed and manufactured by Protarget AG, Germany. The C-TES is designed and produced by CADE Soluciones de Ingenier{\´i}a, S.L., Spain. In the focus of this paper is the description of the operational experience with the PTC, C-TES and boiler during the commissioning and operation phase. Additionally, innovative optimisation measures are presented.}, language = {en} } @inproceedings{RendonSchwagerGhiasietal.2020, author = {Rendon, Carlos and Schwager, Christian and Ghiasi, Mona and Schmitz, Pascal and Bohang, Fakhri and Caminos, Ricardo Alexander Chico and Teixeira Boura, Cristiano Jos{\´e} and Herrmann, Ulf}, title = {Modeling and upscaling of a pilot bayonettube reactor for indirect solar mixed methane reforming}, series = {AIP Conference Proceedings}, booktitle = {AIP Conference Proceedings}, number = {2303}, doi = {10.1063/5.0029974}, pages = {170012-1 -- 170012-9}, year = {2020}, abstract = {A 16.77 kW thermal power bayonet-tube reactor for the mixed reforming of methane using solar energy has been designed and modeled. A test bench for the experimental tests has been installed at the Synlight facility in Juelich, Germany and has just been commissioned. This paper presents the solar-heated reactor design for a combined steam and dry reforming as well as a scaled-up process simulation of a solar reforming plant for methanol production. Solar power towers are capable of providing large amounts of heat to drive high-endothermic reactions, and their integration with thermochemical processes shows a promising future. In the designed bayonet-tube reactor, the conventional burner arrangement for the combustion of natural gas has been substituted by a continuous 930 °C hot air stream, provided by means of a solar heated air receiver, a ceramic thermal storage and an auxiliary firing system. Inside the solar-heated reactor, the heat is transferred by means of convective mechanism mainly; instead of radiation mechanism as typically prevailing in fossil-based industrial reforming processes. A scaled-up solar reforming plant of 50.5 MWth was designed and simulated in Dymola® and AspenPlus®. In comparison to a fossil-based industrial reforming process of the same thermal capacity, a solar reforming plant with thermal storage promises a reduction up to 57 \% of annual natural gas consumption in regions with annual DNI-value of 2349 kWh/m2. The benchmark solar reforming plant contributes to a CO2 avoidance of approx. 79 kilotons per year. This facility can produce a nominal output of 734.4 t of synthesis gas and out of this 530 t of methanol a day.}, language = {en} } @article{GoettscheAlexopoulosDuemmleretal.2019, author = {G{\"o}ttsche, Joachim and Alexopoulos, Spiros and D{\"u}mmler, Andreas and Maddineni, S. K.}, title = {Multi-Mirror Array Calculations With Optical Error}, pages = {1 -- 6}, year = {2019}, abstract = {The optical performance of a 2-axis solar concentrator was simulated with the COMSOL Multiphysics® software. The concentrator consists of a mirror array, which was created using the application builder. The mirror facets are preconfigured to form a focal point. During tracking all mirrors are moved simultaneously in a coupled mode by 2 motors in two axes, in order to keep the system in focus with the moving sun. Optical errors on each reflecting surface were implemented in combination with the solar angular cone of ± 4.65 mrad. As a result, the intercept factor of solar radiation that is available to the receiver was calculated as a function of the transversal and longitudinal angles of incidence. In addition, the intensity distribution on the receiver plane was calculated as a function of the incidence angles.}, language = {en} } @article{GorzalkaSchmiedtSchorn2021, author = {Gorzalka, Philip and Schmiedt, Jacob Estevam and Schorn, Christian}, title = {Automated Generation of an Energy Simulation Model for an Existing Building from UAV Imagery}, series = {Buildings}, volume = {11}, journal = {Buildings}, number = {9}, publisher = {MDPI}, address = {Basel}, issn = {2075-5309}, doi = {10.3390/buildings11090380}, pages = {15 Seiten}, year = {2021}, abstract = {An approach to automatically generate a dynamic energy simulation model in Modelica for a single existing building is presented. It aims at collecting data about the status quo in the preparation of energy retrofits with low effort and costs. The proposed method starts from a polygon model of the outer building envelope obtained from photogrammetrically generated point clouds. The open-source tools TEASER and AixLib are used for data enrichment and model generation. A case study was conducted on a single-family house. The resulting model can accurately reproduce the internal air temperatures during synthetical heating up and cooling down. Modelled and measured whole building heat transfer coefficients (HTC) agree within a 12\% range. A sensitivity analysis emphasises the importance of accurate window characterisations and justifies the use of a very simplified interior geometry. Uncertainties arising from the use of archetype U-values are estimated by comparing different typologies, with best- and worst-case estimates showing differences in pre-retrofit heat demand of about ±20\% to the average; however, as the assumptions made are permitted by some national standards, the method is already close to practical applicability and opens up a path to quickly estimate possible financial and energy savings after refurbishment.}, language = {en} } @article{PeereBlanke2022, author = {Peere, Wouter and Blanke, Tobias}, title = {GHEtool: An open-source tool for borefield sizing in Python}, series = {Journal of Open Source Software}, volume = {7}, journal = {Journal of Open Source Software}, number = {76}, editor = {Vernon, Chris}, issn = {2475-9066}, doi = {10.21105/joss.04406}, pages = {1 -- 4, 4406}, year = {2022}, abstract = {GHEtool is a Python package that contains all the functionalities needed to deal with borefield design. It is developed for both researchers and practitioners. The core of this package is the automated sizing of borefield under different conditions. The sizing of a borefield is typically slow due to the high complexity of the mathematical background. Because this tool has a lot of precalculated data, GHEtool can size a borefield in the order of tenths of milliseconds. This sizing typically takes the order of minutes. Therefore, this tool is suited for being implemented in typical workflows where iterations are required. GHEtool also comes with a graphical user interface (GUI). This GUI is prebuilt as an exe-file because this provides access to all the functionalities without coding. A setup to install the GUI at the user-defined place is also implemented and available at: https://www.mech.kuleuven.be/en/tme/research/thermal_systems/tools/ghetool.}, language = {en} } @inproceedings{BlankeSchmidtGoettscheetal.2022, author = {Blanke, Tobias and Schmidt, Katharina S. and G{\"o}ttsche, Joachim and D{\"o}ring, Bernd and Frisch, J{\´e}r{\^o}me and van Treeck, Christoph}, title = {Time series aggregation for energy system design: review and extension of modelling seasonal storages}, series = {Energy Informatics}, volume = {5}, booktitle = {Energy Informatics}, number = {1, Article number: 17}, editor = {Weidlich, Anke and Neumann, Dirk and Gust, Gunther and Staudt, Philipp and Sch{\"a}fer, Mirko}, publisher = {Springer Nature}, issn = {2520-8942}, doi = {10.1186/s42162-022-00208-5}, pages = {14 Seiten}, year = {2022}, abstract = {Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, "Time series aggregation for energy system design: Modeling seasonal storage", has developed a seasonal storage model to address this issue. Simultaneously, the paper "Optimal design of multi-energy systems with seasonal storage" has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.}, language = {en} }