C Mathematical and Quantitative Methods
Refine
Document Type
- Article (6)
- Conference Proceeding (3)
- Master's Thesis (3)
- Part of a Book (1)
Institute
Keywords
- Energy storage (2)
- Power tracking (2)
- Alterungsstand (1)
- Autonomous optimization (1)
- Casual Game Interaction Design (1)
- Cognitive Load (1)
- Controlling (1)
- Data Science (1)
- Data analytics (1)
- Demand Side Management (1)
Ansätze des maschinellen Lernens werden sowohl in der Forschung als auch in der Praxis eingesetzt, um gewünschte Ausgabedaten anhand bekannter Eingabedaten vorherzusagen. In dieser Masterarbeit wird die Anwendung des maschinellen Lernens in der Batteriedatenanalyse zur Bestimmung des Alterungsstatus von Lithium-Ionen-Batterien untersucht. Das Ziel dieser Arbeit besteht in der Vorhersage von Alterungskurven (englisch state of health - SoH) für Lithium-Ionen Batterien über die Anzahl der Entladezyklen (Zeitachse). Dies erfolgt auf der Grundlage zuvor erfasster Daten für drei Typen von Lithium-Ionen-Batterien, die bei Temperaturen von 15 °C, 25 °C und 35 °C sowie C-Raten von 0,5C, 1C und 2C aufgenommen wurden. Im Zuge dessen wurden die angewandten Methoden des maschinellen Lernens analysiert und ihre Ergebnisse verglichen. Der Umfang dieser Arbeit hebt sich von anderen Ansätzen des maschinellen Lernens in der Batteriedatenanalyse ab, da dieselben Methoden in einem breiteren Spektrum von Daten mit unterschiedlichen Temperaturen und Kathodenmaterialien verwendet wurden. Dies ist für die Analyse von Unterschieden im Verhalten in der Praxis relevant. Nach dem Erwerb und der Vorbereitung der Daten wurden Modelle mit vier ausgewählten Regressionsverfahren (lineare Regression, Ridge-Regression, Random-Forest-Regression und KNN-Regression) des überwachten Lernens trainiert und die Vorhersagen durchgeführt. Aus den Ergebnissen kann eine allgemeingültige Auslegungsgrundlage für weitere Untersuchungen und die praktische Anwendung abgeleitet werden, bei der die Vorhersagen von SoH-Kurven für Lithium-Ionen-Batterien mit linearer Regression und Ridge-Regression die höchste Genauigkeit aufweisen.
Die Anforderungen an gute Prognosen im Energiehandel der illwerke vkw AG steigen kontinuierlich an, da diese dazu verwendet werden, die richtigen Energiemengen auf dem Day-Ahead-Markt zu kaufen oder zu verkaufen. Zusätzliche Herausforderungen wie Wettereinflüsse und der steigende Energiebedarf von E-Autos erschweren die Prognose. Darüber hinaus gestaltet es sich mit den herkömmlichen Prognosebewertungen schwierig, die Kostenaspekte angemessen abzubilden. Aus diesem Grund wird in dieser Masterarbeit eine neue Methode zur Bewertung der Prognosequalität implementiert und mit bewährten Kennzahlen wie R², MAE, MAPE und RMSE verglichen. Diese Methode nutzt einen Preisverlauf, der die durchschnittlichen Marktpreise der Ausgleichsenergiepreise als Bewertungsmaßstab widerspiegelt. Die neue Bewertungsmethode wird mit Algorithmen wie dem Artificial Neural Network von Tensorflow, dem Decision Tree Regressor, der Linearen Regression, dem Multi-Layer Perception und dem Random Forest Regressor von Scikit-Learn verglichen. Zudem wird ein eigens erstelltes Gurobi-Modell, welches die Ausgleichsenergiepreise für die Gewichtung der absoluten Prognosefehler heranzieht, als Lineare Regression implementiert. Die genannten Modelle werden mithilfe von Python implementiert. Es werden tägliche Vorhersagen basierend auf viertelstündlichen Daten für Zeiträume von bis zu einem Jahr unter Verwendung eines Sliding-Window-Verfahrens mit unterschiedlichen Trainingsdaten erstellt. Die neue Bewertungsmethode mit der Einbeziehung von Kostenfaktoren, konnte sich im Vergleich zu MAPE, MAE, RMSE und R² nicht deutlich von den anderen unterscheiden. Die besten Ergebnisse wurden mit der Linearen Regression von Scikit-Learn und dem Gurobi-Modell mit der preisgewichteten Minimierung erzielt. Dabei sind die anderen Algorithmen nicht weit von den Resultaten der LR und GP entfernt. Unter dem Aspekt, dass das eigene Modell die Kosten minimieren soll, konnte es aber nicht als die beste Methode bewertet werden. Deswegen müssen das Modell und die gewählten Ausgleichsenergiepreise optimiert werden. Hierzu erzielte unter den sieben verwendeten Methoden die Lineare Regression das beste Ergebnis.
Tap or swipe
(2023)
The number of electric vehicles will increase rapidly in the coming years. Studies suggest that most owners prefer to charge their electric vehicle at home, which will fuel the need for charging stations in residential complexes where vehicles can be charged overnight. Currently, there already are over 100 such residential complexes, with another 70 added every year in Vorarlberg alone. In most existing residential complexes, however, the grid connections are not sufficient to charge all vehicles at the same time with maximum power. In addition, it is also desirable for grid operators and electricity producers that the power demand be as smooth and predictable as possible. To achieve this, ways to manage flexible loads need to be found, which can operate within the technical constraints. Therefore, the most common scenarios how the load can be made grid-friendly with the help of optional battery storage and/or photovoltaics using optimization methods of linear and stochastic programming were examined. At the same time, the needs of the vehicle owners for charging comfort - namely to find their vehicles reliably charged at the time of their respective departure - were addressed by combining both objectives using suitable weights. The algorithms determined were verified in practice on an existing Vlotte prototype installation. For this purpose, the necessary programs were implemented in Python, so that the data obtained during the test operation, which lasted one month, could be subjected to a well-founded analysis. In addition, simulation studies helped to further reveal the influence of PV and BESS sizing on the achievable optimums and confirm that advanced optimization algorithms such as the ones discussed are a vital contribution in reducing the charging stations’ peak load while at the same time maintaining high satisfaction levels.
Violation-mitigation-based method for PV hosting capacity quantification in low voltage grids
(2022)
Hosting capacity knowledge is of great importance for distribution utilities to assess the amount of PV capacity possible to accommodate without troubling the operation of the grid. In this paper, a novel method to quantify the hosting capacity of low voltage grids is presented. The method starts considering a state of fully exploited building rooftop solar potential. A downward process is proposed - from the starting state with expected violations on the grid operation to a state with no violations. In this process, the installed PV capacity is progressively reduced. The reductions are made sequentially and selectively aiming to mitigate specific violations: nodes overvoltage, lines overcurrent and transformer overloading. Evaluated on real data of fourteen low voltage grids from Austria, the method proposed exhibits benefits in terms of higher hosting capacities and lower computational costs compared to stochastic methods. Furthermore, it also quantifies hosting capacity expansions achievable by overcoming the effect of the violations. The usage of a potential different from solar rooftops is also presented, demonstrating that a user-defined potential allows to quantify the hosting capacity in a more general setting with the method proposed.
Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households’ privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.
The impact of global warming and climate change has forced countries to introduce strict policies and decarbonization goals toward sustainable development. To achieve the decarbonization of the economy, a substantial increase of renewable energy sources is required to meed energy demand and to transition away from fossil fuels. However, renewables are sensitive to environmental conditions, which may lead to imbalances between energy supply and demand. Battery energy storage systems are gaining more attention for balancing energy systems in existing grid networks at various levels such as bulk power management, transmission and distribution, and for end-users. Integrating battery energy storage systems with renewables can also solve reliability issues related to transient energy production and be used as a buffer source for electrical vehicle fast charging. Despite these advantages, batteries are still expensive and typically built for a single application – either for an energy- or power-dense application – which limits economic feasibility and flexibility. This paper presents a theoretical approach of a hybrid energy storage system that utilizes both energy- and power-dense batteries serving multiple grid applications. The proposed system will employ second use electrical vehicle batteries in order to maximise the potential of battery waste. The approach is based on a survey of battery modelling techniques and control methods. It was found that equivalent circuit models as well as unified control methods are best suited for modelling hybrid energy storages for grid applications. This approach for hybrid modelling is intended to help accelerate the renewable energy transition by providing reliable energy storage.
Increasing electric vehicle penetration leads to undesirable peaks in power if no proper coordination in charging is implemented. We tested the feasibility of electric vehicles acting as flexible demands responding to power signals to minimize the system peaks. The proposed hierarchical autonomous demand side management algorithm is formulated as an optimal power tracking problem. The distribution grid operator determines a power signal for filling the valleys in the non-electric vehicle load profile using the electric vehicle demand flexibility and sends it to all electric vehicle controllers. After receiving the control signal, each electric vehicle controller re-scales it to the expected individual electric vehicle energy demand and determines the optimal charging schedule to track the re-scaled signal. No information concerning the electric vehicles are reported back to the utility, hence the approach can be implemented using unidirectional communication with reduced infrastructural requirements. The achieved results show that the optimal power tracking approach has the potential to eliminate additional peak demands induced by electric vehicle charging and performs comparably to its central implementation. The reduced complexity and computational overhead permits also convenient deployment in practice.
PV hosting capacity provides utilities the knowledge of the maximum amount of solar installations possible to accommodate in low voltage grids such that no operational problems arise. As the quantification of the hosting capacity requires data collection, grid modelling, and often time-consuming simulations, simplified estimations for large-scale applications are of interest. In this paper, Bayesian statistical inference is applied to estimate the hosting capacities of more than 5000 real feeders in Austria. The results show that the hosting capacity of 95% of the total feeders can be estimated with a mean error below 20% by only having knowledge of a random sample of 5%. Moreover, the hosting capacity estimation at a regional level shows a maximum error below 9%, also relying on a random sample of 5% of the total feeders. Furthermore, the approach proposed provides a methodology to assess new parameters aiming to improve the accuracy of the hosting capacity estimation at a feeder level.
In the regime of incentive-based autonomous demand response, time dependent prices are typically used to serve as signals from a system operator to consumers. However, this approach has been shown to be problematic from various perspectives. We clarify these shortcomings in a geometric way and thereby motivate the use of power signals instead of price signals. The main contribution of this paper consists of demonstrating in a standard setting that power tracking signals can control flexibilities more efficiently than real-time price signals. For comparison by simulation, German renewable energy production and German standard load profiles are used for daily production and demand profiles, respectively. As for flexibility, an energy storage system with realistic efficiencies is considered. Most critically, the new approach is able to induce consumptions on the demand side that real-time pricing is unable to induce. Moreover, the pricing approach is outperformed with regards to imbalance energy, peak consumption, storage variation, and storage losses without the need for additional communication or computation efforts. It is further shown that the advantages of the optimal power tracking approach compared to the pricing approach increase with the extent of the flexibility. The results indicate that autonomous flexibility control by optimal power tracking is able to integrate renewable energy production efficiently, has additional benefits, and the potential for enhancements. The latter include data uncertainties, systems of flexibilities, and economic implementation.
Die Digitalisierung verändert Geschäftsmodelle und betriebliche Prozesse. Zugleich beeinflussen auch eine verbesserte Datenverfügbarkeit und leistungsfähige analytische Methoden das Controlling und erfordern vermehrt das Einbringen statistischer und informationstechnologischer Fertigkeiten und Kenntnisse. An einem Fallbeispiel aus dem Marketing-Controlling zeigt der Beitrag den Einsatz von Methoden der Business Analytics und thematisiert die Aufgaben des Controllings im digitalen Zeitalter.
For a given set of banks, how big can losses in bad economic or financial scenarios possibly get, and what are these bad scenarios? These are the two central questions of stress tests for banks and the banking system. Current stress tests select stress scenarios in a way which might leave aside many dangerous scenarios and thus create an illusion of safety; and which might consider highly implausible scenarios and thus trigger a false alarm. We show how to select scenarios systematically for a banking system in a context of multiple credit exposures. We demonstrate the application of our method in an example on the Spanish and Italian residential real estate exposures of European banks. Compared to the EBA 2016 stress test our method produces scenarios which are equally plausible as the EBA stress scenario but yield considerably worse system wide losses.
In dieser Arbeit wird Supervised Learning verwendet, um die Zuverlässigkeit von Schweißverbindungen zu evaluieren.
Um die Schweißqualität zu bestimmen, wurden End of Life Tests durchgeführt. Für die statistische Auswertung und Vorhersage der zu erwartenden Lebensdauer, wurden die Daten basierend auf einer logarithmischen Normalverteilung und mit einer multivariablen linearen Regression modelliert. Um die signifikanten Einflussfaktoren zu identifizieren, wurde eine schrittweise Regression genutzt. Die Ergebnisse zeigen, dass das entwickelte Modell die Zuverlässigkeit und Lebensdauer der Schweißverbindung akkurat abbildet und präzise Vorhersagen liefern kann.