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Alleviating the curse of dimensionality in minkowski sum approximations of storage flexibility
(2023)
Many real-world applications require the joint optimization of a large number of flexible devices over some time horizon. The flexibility of multiple batteries, thermostatically controlled loads, or electric vehicles, e.g., can be used to support grid operations and to reduce operation costs. Using piecewise constant power values, the flexibility of each device over d time periods can be described as a polytopic subset in power space. The aggregated flexibility is given by the Minkowski sum of these polytopes. As the computation of Minkowski sums is in general demanding, several approximations have been proposed in the literature. Yet, their application potential is often objective-dependent and limited by the curse of dimensionality. In this paper, we show that up to 2d vertices of each polytope can be computed efficiently and that the convex hull of their sums provides a computationally efficient inner approximation of the Minkowski sum. Via an extensive simulation study, we illustrate that our approach outperforms ten state-of-the-art inner approximations in terms of computational complexity and accuracy for different objectives. Moreover, we propose an efficient disaggregation method applicable to any vertex-based approximation. The proposed methods provide an efficient means to aggregate and to disaggregate typical battery storages in quarter-hourly periods over an entire day with reasonable accuracy for aggregated cost and for peak power optimization.
Vast amounts of oily wastewater are byproducts of the petrochemical and the shipping industry and to this day frequently discharged into water bodies either without or after insufficient treatment. To alleviate the resulting pollution, water treatment processes are in great demand. Bubble column humidifiers (BCHs) as part of humidification–dehumidification systems are predestined for such a task, since they are insensitive to different feed liquids, simple in design and have low maintenance requirements. While humidification in a bubble column has been investigated plentiful for desalination, a systematic investigation of oily wastewater treatment is missing in literature. We filled this gap by analyzing the treatment of an oil–water emulsion experimentally to derive recommendations for future design and operation of BCHs. Our humidity measurements indicate that the air stream is always saturated after humidification for a liquid height of only 10 cm. A residual water mass fraction of 3.5 wt% is measured after a batch run of six hours. Furthermore, continuous measurements show that an increase in oil mass fraction leads to a decrease in system productivity especially for high oil mass fractions. This decrease is caused by the heterogeneity of the liquid temperature profile. A lower liquid height mitigates this heterogeneity, therefore decreasing the heat demand and improving the overall efficiency. The oil content of the produced condensate is below 15 ppm, allowing discharge into various water bodies. The results of our systematic investigation prove suitability and indicate a strong future potential for the use of BCHs in oily wastewater treatment.
Demand-side management approaches that exploit the temporal flexibility of electric vehicles have attracted much attention in recent years due to the increasing market penetration. These demand-side management measures contribute to alleviating the burden on the power system, especially in distribution grids where bottlenecks are more prevalent. Electric vehicles can be defined as an attractive asset for distribution system operators, which have the potential to provide grid services if properly managed. In this thesis, first, a systematic investigation is conducted for two typically employed demand-side management methods reported in the literature: A voltage droop control-based approach and a market-driven approach. Then a control scheme of decentralized autonomous demand side management for electric vehicle charging scheduling which relies on a unidirectionally communicated grid-induced signal is proposed. In all the topics considered, the implications on the distribution grid operation are evaluated using a set of time series load flow simulations performed for representative Austrian distribution grids. Droop control mechanisms are discussed for electric vehicle charging control which requires no communication. The method provides an economically viable solution at all penetrations if electric vehicles charge at low nominal power rates. However, with the current market trends in residential charging equipment especially in the European context where most of the charging equipment is designed for 11 kW charging, the technical feasibility of the method, in the long run, is debatable. As electricity demand strongly correlates with energy prices, a linear optimization algorithm is proposed to minimize charging costs, which uses next-day market prices as the grid-induced incentive function under the assumption of perfect user predictions. The constraints on the state of charge guarantee the energy required for driving is delivered without failure. An average energy cost saving of 30% is realized at all penetrations. Nevertheless, the avalanche effect due to simultaneous charging during low price periods introduces new power peaks exceeding those of uncontrolled charging. This obstructs the grid-friendly integration of electric vehicles.
Power plant operators increasingly rely on predictive models to diagnose and monitor their systems. Data-driven prediction models are generally simple and can have high precision, making them superior to physics-based or knowledge-based models, especially for complex systems like thermal power plants. However, the accuracy of data-driven predictions depends on (1) the quality of the dataset, (2) a suitable selection of sensor signals, and (3) an appropriate selection of the training period. In some instances, redundancies and irrelevant sensors may even reduce the prediction quality.
We investigate ideal configurations for predicting the live steam production of a solid fuel-burning thermal power plant in the pulp and paper industry for different modes of operation. To this end, we benchmark four machine learning algorithms on two feature sets and two training sets to predict steam production. Our results indicate that with the best possible configuration, a coefficient of determination of R^2 = 0.95 and a mean absolute error of MAE=1.2 t/h with an average steam production of 35.1 t/h is reached. On average, using a dynamic dataset for training lowers MAE by 32% compared to a static dataset for training. A feature set based on expert knowledge lowers MAE by an additional 32 %, compared to a simple feature set representing the fuel inputs. We can conclude that based on the static training set and the basic feature set, machine learning algorithms can identify long-term changes. When using a dynamic dataset the performance parameters of thermal power plants are predicted with high accuracy and allow for detecting short-term problems.
Hot water heat pumps are well suited for demand side management, as the heat pump market faced a rapid growth in the past years with the trend to decentralized domestic hot water use. Sales were accelerated through wants and needs of energy conservation, energy efficiency, and less restrictive rules regarding Legionella. While in literature the model predictive control potential for heat pumps is commonly shown in simulations, the share of experimental studies is relatively low. To this day, experimental studies considering solely domestic hot water use are not available. In this paper, the realistic achievable model predictive control potential of a hot water heat pump is compared to the standard hysteresis control, to provide an experimental proof. We show for the first time, how state-of-the-art approaches (model predictive control, system identification, live state estimation, and demand prediction) can be transferred from electric hot water heaters to hot water heat pumps, combined, and implemented into a real-world hot water heat pump setup. The optimization approach, embedded in a realistic experimental setting, leads to a decrease in electric energy demand and cost per unit electricity by approximately 12% and 14%, respectively. Further, an increase in efficiency by approximately 13% has been achieved.
Grey Box models provide an important approach for control analysis in the Heating, Ventilation and Air Conditioning (HVAC) sector. Grey Box models consist of physical models where parameters are estimated from data. Due to the vast amount of component models that can be found in literature, the question arises, which component models perform best on a given system or dataset? This question is investigated systematically using a test case system with real operational data. The test case system consists of a HVAC system containing an energy recovery unit (ER), a heating coil (HC) and a cooling coil (CC). For each component, several suitable model variants from the literature are adapted appropriately and implemented. Four model variants are implemented for the ER and five model variants each for the HC and CC. Further, three global optimization algorithms and four local optimization algorithms to solve the nonlinear least squares system identification are implemented, leading to a total of 700 combinations. The comparison of all variants shows that the global optimization algorithms do not provide significantly better solutions. Their runtimes are significantly higher. Analysis of the models shows a dependency of the model accuracy on the number of total parameters.
Aufgrund des weltweit hohen Wasserverbrauches und des steigenden Rückganges des Grundwassers, wird die Aufbereitung von Abwasser in Zukunft eine immer größere Rolle spielen. Neben großen industriellen Anlagen werden auch dezentrale und mobile Techniken benötigt, um in ländlichen Regionen oder der Schiffahrt Abwässer aufbereiten zu können. In der Schiffahrt treten vor allem ölverschmutzte Abwässer auf. Diese Masterarbeit befasst sich mit dem Betrieb eines Befeuchtungs-Entfeuchtungsprozesses mit Öl-Wasser-Emulsionen. Es wird der Einffluss der Ölkonzentration auf die Prozessparameter sowie die Reinheit des Kondensates und die Effizienz des Prozesses untersucht. Dabei werden mit einem Versuchsstand an der Fachhochschule Vorarlberg Messungen durchgeführt. Anhand der Ergebnisse wird auf das Verhalten des Befeuchtungs-Entfeuchtungsprozesses geschlossen.
Als Öl-Wasser-Emulsion wird eine Mischung aus Paraffinöl und Wasser verwendet, wobei die Mischung auf Volumenprozent basiert. Die Öl-Wasser-Gemische werden in verschiedenen Versuchsreihen in einer Versuchsanlage an der Fachhochschule Vorarlberg betrieben, welche als Befeuchtungs- und Entfeuchtungsanlage konzipiert ist. Dabei wird die Betriebsweise (Batch und kontinuierlich), die Ölkonzentration in der Emulsion und die Prozessparameter wie z. B. Beheizungsleistung variiert. Batch-Versuche werden auf die Konzentration, den Füllstand, die Kondensatproduktion und die Temperaturen über die Zeit betrachtet. Im kontinuierlichen Betrieb wird bei stationärer Betriebsführung die Wärmeübertragung im Befeuchter, Ölrückstände im Kondensat, den Einfluss der Ölkonzentration auf den Dampfdruck der Emulsion, den Einfluss der Ölkonzentration auf die einzubringende Wärmeleistung und die Gained Output Ratio (GOR) der Anlage untersucht. Zudem wird über verschiedene Integrationsansätze die ausgetragene Kondensatmenge ermittelt und mit den gewogenen Werten verglichen. Die Messungen zeigen, dass sich der Befeuchtungs-Entfeuchtungsprozess für die Reinigung von Ölwassern eignet. Eine Aufkonzentrierung der Öl-Wasser-Emulsion ist bis zu ca. 95% möglich. Die steigende Ölkonzentration senkt den Wärmeübergang im Blasensäulenbefeuchter. Bei allen produzierten Kondensatmengen werden Ölrückstände festgestellt, wobei die Ölkonzentration im Kondensat unabhängig von der Ölkonzentration der Emulsion ist. Durch die schlechtere Wärmeübertragung mit steigender Ölkonzentration wird auch der Wärmeeinsatz erhöht. Die GOR wird ab einer Ölkonzentration von 50% in der Emulsion beeinflusst. Eine mathematische Berechnung der Kondensatmenge ist möglich. Dadurch kann auf die Wasserverluste in der Anlage geschlossen werden. Es ist möglich Öl-Wasser-Emulsionen im Befeuchtungs-Entfeuchtungsprozess aufzubereiten. Bei höheren Ölkonzentrationen der Emulsion können lokale Probleme mit Wärmestauungen auftreten. Somit ist eine gut geplante Prozessführung anhand der gezeigten Ergebnisse vorteilhaft.
Die in dieser Arbeit ermittelten Ergebnisse sind für die weitere Forschung mit Öl-Wasser-Emulsionen im Befeuchtungs-Entfeuchtungsprozess hilfreich. Die Messungen zeigen, welche Einflüsse die Ölkonzentration auf den Anlagenbetrieb und die Eigenschaften der Emulsion haben. Die auftretenden Messschwierigkeiten können in weiterführenden Messungen gezielt vermieden oder adjustiert werden.
The ability of water to form cage-like structures and capture gas molecules under high pressure and low temperatures lead to problems in gas pipelines, especially in the mid-20th century. Also, there is an enormous amount of this so-called gas hydrate, captured in deep sea sediments or in terrestrial permafrost soils in which they reserve a possible degradable energy resource. On the other hand, they also maintain a high risk to enhance the ongoing climate change. At the same time, through their high energy storage ability, gas hydrates exhibit a high potential for industrial applications like alternative energy storage, carbon capture technologies or cleaning of exhaust emissions through separation and storage. But through their complex kinetics and ongoing dynamics through induction, synthesis and dissociation, the usage of hydrates is still far away from relevant industrial application. To make the potential capable there is still a huge amount of basic research necessary: Specially to shorten the induction time. An earlier thesis at FH-Vorarlberg exposed a potential method to shorten the induction time through a stirred reactor with an extremely high stirring rate without the usage of promotors. Therefore, this thesis is dedicated to expose the possible reasons for the witnessed effect through high stirring rates (>10000 rpm) at different pressure and tempera-ture conditions. The goal is to show possible physical effects to shorten the induction time of hy-drate synthesis. Therefore, a stirred reactor is used in which the possible effects should be investi-gated through the research with CO2 hydrates. In the research, there will be a closer look on phe-nomena like cavitation, increasing the phase interface through stirring or pressure fluctuations. The results of this thesis show an interesting connection between pressure, stirring rate and increased phase interface. Furthermore, there are also some exposed significances between stirring under spe-cial conditions which were exposed through statistical analyses. The results show that stirring could possibly be a new driving force when executed under the right conditions.
Die CO2 Abscheidung ist ein Schlüsselprozess für die Dekarbonisierung der Wirtschaft und Industrie. Die Entwicklungspfade der IEA und des IPCC zur Erreichung des CO2 Nettonulle-missionsziel bis 2050 oder 2070 beinhalten alle eine Form von Carbon Capture, (CC). Als vielversprechende CC-Technologie gerät die gashydratbasierte CO2 Abscheidung, hbCC, aufgrund der hohen Speicherkapazität bei moderaten Druck- und Temperaturniveau und des unproblematischen Arbeitsmediums Wasser zusehends ins Interesse der Forschung und In-dustrie. Gashydrate sind unstöchiometrische Einschlussverbindungen, bei denen die Gasmo-leküle in einem Wirtsgitter aus Wassermolekülen gespeichert werden können. In einem m3 Gashydrat können 170 Nm3 Gas gespeichert werden. Die statischen Eigenschaften von Gas-hydrat sind gut verstanden. Die Dynamik der Synthese und Dissoziation, die intrinsische Re-aktionskinetik der Hydratformation, die Nukleation von initialen Kristallisationskeimen und der Einfluss von Wärme- und Stofftransportphänomenen auf die Dynamik ist noch nicht geklärt. Ein profundes Verständnis der Synthese- und Dissoziationsdynamik, inklusive dem Zusam-menhang mit den p,T-Prozessbedingungen, gilt als Voraussetzung für die Entwicklung effizi-enter hbCC-Verfahren. Üblicherweise wird Gashydrat synthetisiert indem flüssiges Wasser mit der Gasphase in Kontakt gebracht wird. Der initial gebildete Hydratfilm auf der Phasen-grenzfläche hemmt in weiter Folge den Stofftransport für das weitere Hydratwachstum. Die CO2 Gasphasenabscheidung durch thermisches Verdampfen unter Druck, (engl. pressurized thermal evaporation, PTE), unterliegt keinem gehemmten Stofftransport, weil Wasserdampf und Gasmoleküle an einer kalten Substratoberfläche kontinuierlich für die Synthese vorliegen. In vorhergehenden Studien wurden subsequente Synthese- und Dissoziationsexperimente durch PTE aus reiner CO2 oder CH4 Gasphase zur Untersuchung der Dynamik durchgeführt. Für diese Arbeit werden erstmals subsequente PTE Synthese- und Dissoziationsexperimente aus einem binären 0,85 N2 + 0,15 CO2 Synthesegasgemisch umgesetzt. Das durch die Syn-these abgeschiedene Gas wird nach der Dissoziation mit einem Massenspektrometer auf seine Zusammensetzung untersucht. Hydratspeicherkapazität, Abscheiderate und die Selek-tivität der CO2 Gasphasenabscheidung wird für eine Synthesetemperaturvariation, (- 40 °C bis - 15 °C), und einen Synthesedruck von 40 bar(a) bestimmt. Durch Zeitrafferauf-nahmen der Hydratformation und Dissoziation wird die Auswirkung der p,T-Prozessbedingun-gen auf die Synthese- und Dissoziationsdynamik untersucht und der optimale Betriebspunkt für die CO2 Gasphasenabscheidung durch thermisches Verdampfen unter Druck bestimmt. Aus den Ergebnissen lässt sich ein klarer Zusammenhang zwischen Synthesetemperatur, Ab-scheiderate und Selektivität ableiten. Ein tiefere Synthesetemperatur führt zu einer effiziente-ren CO2 Abscheidung. Außerdem zeigt sich bei der Beobachtung der Synthesedynamik eine direkte Resublimation des Gashydrats auf der Wachstumsoberfläche. Es bildet sich keine flüssige Übergangsphase vor der Nukleation. Die neuen Erkenntnisse sind wichtige Faktoren für das Design zukünftiger PTE-Verfahren und Prototypen.
Flexibility estimation is the first step necessary to incorporate building energy systems into demand side management programs. We extend a known method for temporal flexibility estimation from literature to a real-world residential heat pump system, solely based on historical cloud data. The method proposed relies on robust simplifications and estimates employing process knowledge, energy balances and manufacturer's information. Resulting forced and delayed temporal flexibility, covering both domestic hot water and space heating demands as constraints, allows to derive a flexibility range for the heat pump system. The resulting temporal flexibility lay within the range of 24 minutes and 6 hours for forced and delayed flexibility, respectively. This range provides new insights into the system's behaviour and is the basis for estimating power and energy flexibility - the first step necessary to incorporate building energy systems into demand side management programs.