@inproceedings{ThomaStiemerBraunetal.2023, author = {Thoma, Andreas and Stiemer, Luc and Braun, Carsten and Fisher, Alex and Gardi, Alessandro G.}, title = {Potential of hybrid neural network local path planner for small UAV in urban environments}, series = {AIAA SCITECH 2023 Forum}, booktitle = {AIAA SCITECH 2023 Forum}, publisher = {AIAA}, address = {Reston, Va.}, doi = {10.2514/6.2023-2359}, pages = {13 Seiten}, year = {2023}, abstract = {This work proposes a hybrid algorithm combining an Artificial Neural Network (ANN) with a conventional local path planner to navigate UAVs efficiently in various unknown urban environments. The proposed method of a Hybrid Artificial Neural Network Avoidance System is called HANNAS. The ANN analyses a video stream and classifies the current environment. This information about the current Environment is used to set several control parameters of a conventional local path planner, the 3DVFH*. The local path planner then plans the path toward a specific goal point based on distance data from a depth camera. We trained and tested a state-of-the-art image segmentation algorithm, PP-LiteSeg. The proposed HANNAS method reaches a failure probability of 17\%, which is less than half the failure probability of the baseline and around half the failure probability of an improved, bio-inspired version of the 3DVFH*. The proposed HANNAS method does not show any disadvantages regarding flight time or flight distance.}, language = {en} } @inproceedings{ChircuCzarneckiFriedmannetal.2023, author = {Chircu, Alina and Czarnecki, Christian and Friedmann, Daniel and Pomaskow, Johanna and Sultanow, Eldar}, title = {Towards a Digital Twin of Society}, series = {Proceedings of the 56th Hawaii International Conference on System Sciences 2023}, booktitle = {Proceedings of the 56th Hawaii International Conference on System Sciences 2023}, publisher = {University of Hawai'i}, address = {Honolulu}, isbn = {978-0-9981331-6-4}, pages = {6748 -- 6757}, year = {2023}, abstract = {This paper describes the potential for developing a digital twin of society- a dynamic model that can be used to observe, analyze, and predict the evolution of various societal aspects. Such a digital twin can help governmental agencies and policy makers in interpreting trends, understanding challenges, and making decisions regarding investments or policies necessary to support societal development and ensure future prosperity. The paper reviews related work regarding the digital twin paradigm and its applications. The paper presents a motivating case study- an analysis of opportunities and challenges faced by the German federal employment agency, Bundesagentur f¨ur Arbeit (BA), proposes solutions using digital twins, and describes initial proofs of concept for such solutions.}, 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{Gaigall2023, author = {Gaigall, Daniel}, title = {Allocating and forecasting changes in risk}, series = {Journal of risk}, volume = {25}, journal = {Journal of risk}, number = {3}, editor = {AitSahlia, Farid}, publisher = {Infopro Digital Risk}, address = {London}, issn = {1755-2842}, doi = {10.21314/JOR.2022.048}, pages = {1 -- 24}, year = {2023}, abstract = {We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio's components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio's components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.}, language = {en} } @inproceedings{TranTrinhDaoetal.2022, author = {Tran, Ngoc Trinh and Trinh, Tu Luc and Dao, Ngoc Tien and Giap, Van Tan and Truong, Manh Khuyen and Dinh, Thuy Ha and Staat, Manfred}, title = {Limit and shakedown analysis of structures under random strength}, series = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training}, booktitle = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training}, publisher = {Nha xuat ban Khoa hoc tu nhien va Cong nghe (Verlag Naturwissenschaft und Technik)}, address = {Hanoi}, isbn = {978-604-357-084-7}, pages = {510 -- 518}, year = {2022}, abstract = {Direct methods comprising limit and shakedown analysis is a branch of computational mechanics. It plays a significant role in mechanical and civil engineering design. The concept of direct method aims to determinate the ultimate load bearing capacity of structures beyond the elastic range. For practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and onstraints. If strength and loading are random quantities, the problem of shakedown analysis is considered as stochastic programming. This paper presents a method so called chance constrained programming, an effective method of stochastic programming, to solve shakedown analysis problem under random condition of strength. In this our investigation, the loading is deterministic, the strength is distributed as normal or lognormal variables.}, language = {en} } @article{Gaigall2023, author = {Gaigall, Daniel}, title = {On the applicability of several tests to models with not identically distributed random effects}, series = {Statistics : A Journal of Theoretical and Applied Statistics}, volume = {57}, journal = {Statistics : A Journal of Theoretical and Applied Statistics}, publisher = {Taylor \& Francis}, address = {London}, isbn = {0323-3944}, issn = {1029-4910}, doi = {10.1080/02331888.2023.2193748}, pages = {14 Seiten}, year = {2023}, abstract = {We consider Kolmogorov-Smirnov and Cram{\´e}r-von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.}, language = {en} } @misc{WiegnerVolkerMainzetal.2022, author = {Wiegner, J. and Volker, H. and Mainz, F. and Backes, A. and L{\"o}ken, M. and H{\"u}ning, Felix}, title = {Wiegand-Effect-Powered Wireless IT Sensor Node}, year = {2022}, abstract = {With the growing interest in small distributed sensors for the "Internet of Things", more attention is being paid to energy harvesting techologies. Reducing or eliminating the need for external power sources or batteries make devices more self-sufficient, more reliable, and reduces maintenance requirements. The Wiegand effect is a proven technology for harvesting small amounts of electrical power from mechanical motion.}, language = {en} } @article{FalkenbergVossBottetal.2023, author = {Falkenberg, Fabian and Voß, Leonie and Bott, Michael and Bongaerts, Johannes and Siegert, Petra}, title = {New robust subtilisins from halotolerant and halophilic Bacillaceae}, series = {Applied Microbiology and Biotechnology}, volume = {107}, journal = {Applied Microbiology and Biotechnology}, publisher = {Springer Nature}, address = {Berlin}, issn = {1432-0614}, doi = {10.1007/s00253-023-12553-w}, pages = {3939 -- 3954}, year = {2023}, abstract = {The aim of the present study was the characterisation of three true subtilisins and one phylogenetically intermediate subtilisin from halotolerant and halophilic microorganisms. Considering the currently growing enzyme market for efficient and novel biocatalysts, data mining is a promising source for novel, as yet uncharacterised enzymes, especially from halophilic or halotolerant Bacillaceae, which offer great potential to meet industrial needs. Both halophilic bacteria Pontibacillus marinus DSM 16465ᵀ and Alkalibacillus haloalkaliphilus DSM 5271ᵀ and both halotolerant bacteria Metabacillus indicus DSM 16189 and Litchfieldia alkalitelluris DSM 16976ᵀ served as a source for the four new subtilisins SPPM, SPAH, SPMI and SPLA. The protease genes were cloned and expressed in Bacillus subtilis DB104. Purification to apparent homogeneity was achieved by ethanol precipitation, desalting and ion-exchange chromatography. Enzyme activity could be observed between pH 5.0-12.0 with an optimum for SPPM, SPMI and SPLA around pH 9.0 and for SPAH at pH 10.0. The optimal temperature for SPMI and SPLA was 70 °C and for SPPM and SPAH 55 °C and 50 °C, respectively. All proteases showed high stability towards 5\% (w/v) SDS and were active even at NaCl concentrations of 5 M. The four proteases demonstrate potential for future biotechnological applications.}, language = {en} } @inproceedings{KreyerEsch2017, author = {Kreyer, J{\"o}rg and Esch, Thomas}, title = {Simulation Tool for Predictive Control Strategies for an ORCSystem in Heavy Duty Vehicles}, series = {European GT Conference 2017}, booktitle = {European GT Conference 2017}, pages = {16 Seiten}, year = {2017}, abstract = {Scientific questions - How can a non-stationary heat offering in the commercial vehicle be used to reduce fuel consumption? - Which potentials offer route and environmental information among with predicted speed and load trajectories to increase the efficiency of a ORC-System? Methods - Desktop bound holistic simulation model for a heavy duty truck incl. an ORC System - Prediction of massflows, temperatures and mixture quality (AFR) of exhaust gas}, language = {en} } @techreport{EschFunkeRoosen2010, author = {Esch, Thomas and Funke, Harald and Roosen, Petra}, title = {SIoBiA - Safety Implications of Biofuels in Aviation}, publisher = {EASA}, address = {K{\"o}ln}, pages = {279 Seiten}, year = {2010}, abstract = {Biofuels potentially interesting also for aviation purposes are predominantly liquid fuels produced from biomass. The most common biofuels today are biodiesel and bioethanol. Since diesel engines are rather rare in aviation this survey is focusing on ethanol admixed to gasoline products. The Directive 2003/30/EC of the European Parliament and the Council of May 8th 2003 on the promotion of the use of biofuels or other renewable fuels for transport encourage a growing admixture of biogenic fuel components to fossil automotive gasoline. Some aircraft models equipped with spark ignited piston engines are approved for operation with automotive gasoline, frequently called "MOGAS" (motor gasoline). The majority of those approvals is limited to MOGAS compositions that do not contain methanol or ethanol beyond negligible amounts. In the past years (bio-)MTBE or (bio-)ETBE have been widely used as blending component of automotive gasoline whilst the usage of low-molecular alcohols like methanol or ethanol has been avoided due to the handling problems especially with regard to the strong affinity for water. With rising mandatory bio-admixtures the conversion of the basic biogenic ethanol to ETBE, causing a reduction of energetic payoff, becomes more and more unattractive. Therefore the direct ethanol admixture is accordingly favoured. Due to the national enforcements of the directive 2003/30/EC more oxygenates produced from organic materials like bioethanol have started to appear in automotive gasolines already. The current fuel specification EN 228 already allows up to 3 \% volume per volume (v/v) (bio-)methanol or up to 5 \% v/v (bio-)ethanol as fuel components. This is also roughly the amount of biogenic components to comply with the legal requirements to avoid monetary penalties for producers and distributors of fuels. Since automotive fuel is cheaper than the common aviation gasoline (AVGAS), creates less problems with lead deposits in the engine, and in general produces less pollutants it is strongly favoured by pilots. But being designed for a different set of usage scenarios the use of automotive fuel with low molecular alcohols for aircraft operation may have adverse effects in aviation operation. Increasing amounts of ethanol admixtures impose various changes in the gasoline's chemical and physical properties, some of them rather unexpected and not within the range of flight experiences even of long-term pilots.}, language = {en} } @article{Esch2010, author = {Esch, Thomas}, title = {Trends in commercial vehicle powertrains}, series = {ATZautotechnology}, volume = {2010}, journal = {ATZautotechnology}, number = {10}, publisher = {Vieweg \& Sohn}, address = {Wiesbaden}, issn = {2192-886X}, doi = {10.1007/BF03247185}, pages = {26 -- 31}, year = {2010}, abstract = {Low emission zones and truck bans, the rising price of diesel and increases in road tolls: all of these factors are putting serious pressure on the transport industry. Commercial vehicle manufacturers and their suppliers are in the process of identifying new solutions to these challenges as part of their efforts to meet the EEV (enhanced environmentally friendly vehicle) limits, which are currently the most robust European exhaust and emissions standards for trucks and buses.}, language = {en} } @inproceedings{KemperHellenbroichEsch2009, author = {Kemper, Hans and Hellenbroich, Gereon and Esch, Thomas}, title = {Concept of an innovative passenger-car hybrid drive for European driving conditions}, series = {Hybrid vehicles and energy management : 6th symposium ; 18th and 19th February 2009, Stadthalle Braunschweig}, booktitle = {Hybrid vehicles and energy management : 6th symposium ; 18th and 19th February 2009, Stadthalle Braunschweig}, publisher = {Gesamtzentrum f{\"u}r Verkehr (GZVB)}, address = {Braunschweig}, isbn = {978-3-937655-20-8}, pages = {264 -- 287}, year = {2009}, abstract = {The downsizing of spark ignition engines in conjunction with turbocharging is considered to be a promising method for reducing CO₂ emissions. Using this concept, FEV has developed a new, highly efficient drivetrain to demonstrate fuel consumption reduction and drivability in a vehicle based on the Ford Focus ST. The newly designed 1.8L turbocharged gasoline engine incorporates infinitely variable intake and outlet control timing and direct fuel injection utilizing piezo injectors centrally located. In addition, this engine uses a prototype FEV engine control system, with software that was developed and adapted entirely by FEV. The vehicle features a 160 kW engine with a maximum mean effective pressure of 22.4 bar and 34 \% savings in simulated fuel consumption. During the first stage, a new electrohydraulically actuated hybrid transmission with seven forward gears and one reverse gear and a single dry starting clutch will be integrated. The electric motor of the hybrid is directly connected to the gear set of the transmission. Utilizing the special gear set layout, the electric motor can provide boost during a change of gears, so that there is no interruption in traction. Therefore, the transmission system combines the advantages of a double clutch controlled gear change (gear change without an interruption in traction) with the efficient, cost-effective design of an automated manual transmission system. Additionally, the transmission provides a purely electric drive system and the operation of an air-conditioning compressor during the engine stop phases. One other alternative is through the use of CAI (Controlled Auto Ignition), which incorporates a process developed by FEV for controlled compression ignition.}, language = {en} } @inproceedings{FunkeEschRoosen2009, author = {Funke, Harald and Esch, Thomas and Roosen, Peter}, title = {Using motor gasoline for aircrafts - coping with growing bio-fuel-caused risks by understanding cause-effect relationship}, series = {Fuels 2009 : mineral oil based and alternative fuels ; 7th international colloquium ; January 14 - 15, 2009}, booktitle = {Fuels 2009 : mineral oil based and alternative fuels ; 7th international colloquium ; January 14 - 15, 2009}, editor = {Bartz, Wilfried J.}, publisher = {Technische Akademie Esslingen (TAE)}, address = {Ostfildern}, isbn = {978-3-924813-75-8}, pages = {237 -- 244}, year = {2009}, abstract = {The utilisation of vehicle-oriented gasoline in general aviation is very desirable for both ecological and economical reasons, as well as for general considerations of availability. As of today vehicle fuels may be used if the respective engine and cell are certified for such an operation. For older planes a supplementary technical certificate is provided for gasoline mixtures with less than 1 \% v/v ethanol only, though. Larger admixtures of ethanol may lead to sudden engine malfunction and should be considered as considerable security risks. Major problems are caused by the partially ethanol non-withstanding materials, a necessarily changed stochiometric adjustment of the engine for varying ethanol shares and the tendency for phase separation in the presence of absorbed water. The concepts of the flexible fuel vehicles are only partially applicable in the view of air security.}, language = {en} } @inproceedings{AltherrConzenElsenetal.2023, author = {Altherr, Lena and Conzen, Max and Elsen, Ingo and Frauenrath, Tobias and Lyrmann, Andreas}, title = {Sensor retrofitting of existing buildings in an interdisciplinary teaching project at university level}, series = {Tagungsband AALE 2023 : mit Automatisierung gegen den Klimawandel}, booktitle = {Tagungsband AALE 2023 : mit Automatisierung gegen den Klimawandel}, editor = {Reiff-Stephan, J{\"o}rg and J{\"a}kel, Jens and Schwarz, Andr{\´e}}, publisher = {le-tex publishing services GmbH}, address = {Leipzig}, isbn = {978-3-910103-01-6}, doi = {10.33968/2023.04}, pages = {31 -- 40}, year = {2023}, abstract = {Existing residential buildings have an average lifetime of 100 years. Many of these buildings will exist for at least another 50 years. To increase the efficiency of these buildings while keeping costs at reasonable rates, they can be retrofitted with sensors that deliver information to central control units for heating, ventilation and electricity. This retrofitting process should happen with minimal intervention into existing infrastructure and requires new approaches for sensor design and data transmission. At FH Aachen University of Applied Sciences, students of different disciplines work together to learn how to design, build, deploy and operate such sensors. The presented teaching project already created a low power design for a combined CO2, temperature and humidity measurement device that can be easily integrated into most home automation systems}, language = {en} } @inproceedings{Maurer2022, author = {Maurer, Florian}, title = {Framework to provide a simulative comparison of different energy market designs}, series = {Energy Informatics}, volume = {5}, booktitle = {Energy Informatics}, number = {2, Article number: 12}, publisher = {Springer Nature}, issn = {2520-8942}, doi = {10.1186/s42162-022-00215-6}, pages = {18 -- 20}, year = {2022}, abstract = {Useful market simulations are key to the evaluation of diferent market designs existing of multiple market mechanisms or rules. Yet a simulation framework which has a comparison of diferent market mechanisms in mind was not found. The need to create an objective view on different sets of market rules while investigating meaningful agent strategies concludes that such a simulation framework is needed to advance the research on this subject. An overview of diferent existing market simulation models is given which also shows the research gap and the missing capabilities of those systems. Finally, a methodology is outlined how a novel market simulation which can answer the research questions can be developed.}, language = {en} } @inproceedings{DeyElsenFerreinetal.2021, author = {Dey, Thomas and Elsen, Ingo and Ferrein, Alexander and Frauenrath, Tobias and Reke, Michael and Schiffer, Stefan}, title = {CO2 Meter: a do-it-yourself carbon dioxide measuring device for the classroom}, series = {PETRA '21: Proceedings of the 14th Pervasive Technologies Related to Assistive Environments Conference}, booktitle = {PETRA '21: Proceedings of the 14th Pervasive Technologies Related to Assistive Environments Conference}, editor = {Makedon, Fillia}, publisher = {Association for Computing Machinery}, address = {New York}, isbn = {9781450387927}, doi = {10.1145/3453892.3462697}, pages = {292 -- 299}, year = {2021}, abstract = {In this paper we report on CO2 Meter, a do-it-yourself carbon dioxide measuring device for the classroom. Part of the current measures for dealing with the SARS-CoV-2 pandemic is proper ventilation in indoor settings. This is especially important in schools with students coming back to the classroom even with high incidents rates. Static ventilation patterns do not consider the individual situation for a particular class. Influencing factors like the type of activity, the physical structure or the room occupancy are not incorporated. Also, existing devices are rather expensive and often provide only limited information and only locally without any networking. This leaves the potential of analysing the situation across different settings untapped. Carbon dioxide level can be used as an indicator of air quality, in general, and of aerosol load in particular. Since, according to the latest findings, SARS-CoV-2 can be transmitted primarily in the form of aerosols, carbon dioxide may be used as a proxy for the risk of a virus infection. Hence, schools could improve the indoor air quality and potentially reduce the infection risk if they actually had measuring devices available in the classroom. Our device supports schools in ventilation and it allows for collecting data over the Internet to enable a detailed data analysis and model generation. First deployments in schools at different levels were received very positively. A pilot installation with a larger data collection and analysis is underway.}, language = {en} } @article{ElsenHartungHornetal.2001, author = {Elsen, Ingo and Hartung, Frank and Horn, Uwe and Kampmann, Markus and Peters, Liliane}, title = {Streaming technology in 3G mobile communication systems}, series = {Computer : innovative technology for computer professionals}, volume = {34}, journal = {Computer : innovative technology for computer professionals}, number = {9 Seiten}, editor = {Voas, Jeffrey}, publisher = {IEEE}, address = {New York}, issn = {0018-9162}, pages = {46 -- 52}, year = {2001}, abstract = {Third-generation mobile communication systems will combine standardized streaming with a range of unique services to provide high-quality Internet content that meets the specific needs of the rapidly growing mobile market.}, language = {en} } @article{FunkeEschRoosen2022, author = {Funke, Harald and Esch, Thomas and Roosen, Petra}, title = {Powertrain Adaptions for LPG Usage in General Aviation}, series = {MTZ worldwide}, volume = {2022}, journal = {MTZ worldwide}, number = {83}, publisher = {Springer Nature}, address = {Basel}, doi = {10.1007/s38313-021-0756-6}, pages = {58 -- 62}, year = {2022}, abstract = {In general aviation, too, it is desirable to be able to operate existing internal combustion engines with fuels that produce less CO₂ than Avgas 100LL being widely used today It can be assumed that, in comparison, the fuels CNG, LPG or LNG, which are gaseous under normal conditions, produce significantly lower emissions. Necessary propulsion system adaptations were investigated as part of a research project at Aachen University of Applied Sciences.}, 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} }