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This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.
Batteries typically consist of multiple individual cells connected in series. Here we demonstrate single-cell state of charge (SOC) and state of health (SOH) diagnosis in a 24 V class lithium-ion battery. To this goal, we introduce and apply a novel, highly efficient algorithm based on a voltage-controlled model (VCM). The battery, consisting of eight single cells, is cycled over a duration of five months under a simple cycling protocol between 20 % and 100 % SOC. The cell-to-cell standard deviations obtained with the novel algorithm were 1.25 SOC-% and 1.07 SOH-% at beginning of cycling. A cell-averaged capacity loss of 9.9 % after five months cycling was observed. While the accuracy of single-cell SOC estimation was limited (probably owed to the flat voltage characteristics of the lithium iron phosphate, LFP, chemistry investigated here), single-cell SOH estimation showed a high accuracy (2.09 SOH-% mean absolute error compared to laboratory reference tests). Because the algorithm does not require observers, filters, or neural networks, it is computationally very efficient (three seconds analysis time for the complete data set consisting of eight cells with approx. 780.000 measurement points per cell).
Variable refrigerant flow (VRF) and variable air volume (VAV) systems are considered among the best heating, ventilation, and air conditioning systems (HVAC) thanks to their ability to provide cooling and heating in different thermal zones of the same building. As well as their ability to recover the heat rejected from spaces requiring cooling and reuse it to heat another space. Nevertheless, at the same time, these systems are considered one of the most energy-consuming systems in the building. So, it is crucial to well size the system according to the building’s cooling and heating needs and the indoor temperature fluctuations. This study aims to compare these two energy systems by conducting an energy model simulation of a real building under a semi-arid climate for cooling and heating periods. The developed building energy model (BEM) was validated and calibrated using measured and simulated indoor air temperature and energy consumption data. The study aims to evaluate the effect of these HVAC systems on energy consumption and the indoor thermal comfort of the building. The numerical model was based on the Energy Plus simulation engine. The approach used in this paper has allowed us to reach significant quantitative energy saving along with a high level of indoor thermal comfort by using the VRF system compared to the VAV system. The findings prove that the VRF system provides 46.18% of the annual total heating energy savings and 6.14% of the annual cooling and ventilation energy savings compared to the VAV system.
Lithium-ion batteries exhibit slow voltage dynamics on the minute time scale that are usually associated with transport processes. We present a novel modelling approach toward these dynamics by combining physical and data-driven models into a Grey-box model. We use neural networks, in particular neural ordinary differential equations. The physical structure of the Grey-box model is borrowed from the Fickian diffusion law, where the transport domain is discretized using finite volumes. Within this physical structure, unknown parameters (diffusion coefficient, diffusion length, discretization) and dependencies (state of charge, lithium concentration) are replaced by neural networks and learnable parameters. We perform model-to-model comparisons, using as training data (a) a Fickian diffusion process, (b) a Warburg element, and (c) a resistor-capacitor circuit. Voltage dynamics during constant-current operation and pulse tests as well as electrochemical impedance spectra are simulated. The slow dynamics of all three physical models in the order of ten to 30 min are well captured by the Grey-box model, demonstrating the flexibility of the present approach.
This article presents the development, parameterization, and experimental validation of a pseudo-three-dimensional (P3D) multiphysics aging model of a 500 mAh high-energy lithium-ion pouch cell with graphite negative electrode and lithium nickel manganese cobalt oxide (NMC) positive electrode. This model includes electrochemical reactions for solid electrolyte interphase (SEI) formation at the graphite negative electrode, lithium plating, and SEI formation on plated lithium. The thermodynamics of the aging reactions are modeled depending on temperature and ion concentration and the reactions kinetics are described with an Arrhenius-type rate law. Good agreement of model predictions with galvanostatic charge/discharge measurements and electrochemical impedance spectroscopy is observed over a wide range of operating conditions. The model allows to quantify capacity loss due to cycling near beginning-of-life as function of operating conditions and the visualization of aging colormaps as function of both temperature and C-rate (0.05 to 2 C charge and discharge, −20 °C to 60 °C). The model predictions are also qualitatively verified through voltage relaxation, cell expansion and cell cycling measurements. Based on this full model, six different aging indicators for determination of the limits of fast charging are derived from post-processing simulations of a reduced, pseudo-two-dimensional isothermal model without aging mechanisms. The most successful aging indicator, compared to results from the full model, is based on combined lithium plating and SEI kinetics calculated from battery states available in the reduced model. This methodology is applicable to standard pseudo-two-dimensional models available today both commercially and as open source.
Predictive control has great potential in the home energy management domain. However, such controls need reliable predictions of the system dynamics as well as energy consumption and generation, and the actual implementation in the real system is associated with many challenges. This paper presents the implementation of predictive controls for a heat pump with thermal storage in a real single-family house with a photovoltaic rooftop system. The predictive controls make use of a novel cloud camera-based short-term solar energy prediction and an intraday prediction system that includes additional data sources. In addition, machine learning methods were used to model the dynamics of the heating system and predict loads using extensive measured data. The results of the real and simulated operation will be presented.
Photovoltaic-heat pump (PV-HP) combinations with battery and energy management systems are becoming increasingly popular due to their ability to increase the autarchy and utilization of self-generated PV electricity. This trend is driven by the ongoing electrification of the heating sector and the growing disparity between growing electricity costs and reducing feed-in tariffs in Germany. Smart control strategies can be employed to control and optimize the heat pump operation to achieve higher self-consumption of PV electricity. This work presents the evaluation results of a smart-grid ready controlled PV-HP-battery system in a single-family household in Germany, using 1-minute-high-resolution field measurement data. Within 12 months evaluation period, a self-consumption of 43% was determined. The solar fraction of the HP amounts to 36%, enabled also due to higher set temperatures for space heating and domestic hot water production. Accordingly, the SPF decreases by 4.0% the space heating and by 5.7% in the domestic hot water mode. The combined seasonal performance factor for the heat pump system increases from 4.2 to 6.7, when only considering the electricity taken from the grid and disregarding the locally generated electricity supplied from photovoltaic and battery units.
Photovoltaic thermal (PVT) technology has been drawing attention recently. Electrification of the heating sector with heat pumps run by carbon-free electricity sources like photovoltaics is setting the ground for the interest. This article gives insight into PVT technologies and collector designs according to application and operating temperatures. For most conventional designs, examples like prototypes from Research & Development projects are presented. In addition, commercial products are listed along these categories, and the influence on the gross thermal and electrical yield is depicted based on Solar Keymark certification data. The process of certification is presented in a comprehensive way, showing current limitations, giving an outlook on the most recent approach for enhanced procedures and specifications. Finally, different system layouts are presented, and examples from installations combined with a heat pump are given with their specific performances. Real performance data of several PVT installations are compared to conventional heat pump systems. The identified seasonal performance factors are in a range from 3.4 to 4.2 and in between air source and ground source heat pumps. Continuous monitoring and derived data are enablers to discover the decisive influence of the system layout and dimensioning on performance indicators like, for example, operating temperatures over the year.
With the function RooTri(), we present a simple and robust calculation method for the approximation of the intersection points of a scalar field given as an unstructured point cloud with a plane oriented arbitrarily in space. The point cloud is approximated to a surface consisting of triangles whose edges are used for computing the intersection points. The function contourc() of Matlab is taken as a reference. Our experiments show that the function contourc() produces outliers that deviate significantly from the defined nominal value, while the quality of the results produced by the function RooTri() increases with finer resolution of the examined grid.
Ziel der vorliegenden Arbeit ist das netzdienliche Betreiben einer Wärmepumpe. Um diese Netzdienlichkeit zu erreichen, wird ein modellprädiktiver Regler entwickelt und implementiert, dessen Ziel es ist die Stromkosten einer Wärmepumpe zu senken. Dazu werden die Variablen Stromkosten und ein simulierter Heizbetrieb betrachtet.
Die Entwicklung eines modellprädiktiven Reglers setzt zunächst eine Modellierung der Komponenten des Heizsystems voraus. Ebenfalls muss eine Kostenfunktion formuliert werden, die es zu minimieren gilt. In einem Optimierungsproblem werden die Modelle als Randbedingungen und die Kostenfunktion als Zielfunktion der Optimierung formuliert. Dazu müssen gewisse Vereinfachungen getroffen werden, um das Optimierungsproblem zuverlässig und ohne enormen Rechenaufwand in einer Regelungsschleife lösen zu können.
Nun wird das Optimierungsproblem mit externen Modulen verknüpft, die eine Kommunikation mit der realen Wärmepumpen, Strompreisprognosen und Wettervorhersagen ermöglichen. Der dabei entwickelte Algorithmus wird auf einem Raspberry Pi Einplatinencomputer gespeichert und dort in einem regelmäßigen Zeitintervall von 15 Minuten ausgeführt, um den Betrieb der Wärmepumpe zu regeln.
Schließlich wird der modellprädiktive Regler in Betrieb genommen. Anschließend kann der modellprädiktive Betrieb mit dem konventionellen Betrieb verglichen werden. Aus dem Vergleich wird deutlich, dass eine modellprädiktive Regelung tatsächlich die Netzdienlichkeit einer Wärmepumpe verbessern kann. Andererseits werden auch die Entwicklungspotentiale identifiziert.