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This work introduced the reader to all relevant fields to tap into an ultrasound-based state of charge estimation and provides a blueprint for the procedure to achieve and test the fundamentals of such an approach. It spanned from an in-depth electrochemical characterization of the studied battery cells over establishing the measurement technique, digital processing of ultrasonic transmission signals, and characterization of the SoC dependent property changes of those signals to a proof of concept of an ultrasound-based state of charge estimation.
The State of the art & theoretical background chapter focused on the battery section on the mechanical property changes of lithium-ion batteries during operation. The components and the processes involved to manufacture a battery cell were described to establish the fundamentals for later interrogation. A comprehensive summary of methods for state estimation was given and an emphasis was laid on mechanical methods, including a critical review of the most recent research on ultrasound-based state estimation. Afterward, the fundamentals of ultrasonic non-destructive evaluation were introduced, starting with the sound propagation modes in isotropic boundary-free media, followed by the introduction of boundaries and non-isotropic structure to finally approach the class of fluid-saturated porous media, which batteries can be counted to. As the processing of the ultrasonic signals transmitted through lithium-ion battery cells with the aim of feature extraction was one of the main goals of this work, the fundamentals of digital signal processing and methods for the time of flight estimation were reviewed and compared in a separate section.
All available information on the interrogated battery cell and the instrumentation was collected in the Experimental methods & instrumentation chapter, including a detailed step-by-step manual of the process developed in this work to create and attach a sensor stack for ultrasonic interrogation based on low-cost off-the-shelf piezo elements.
The Results & discussion chapter opened with an in-depth electrochemical and post-mortem interrogation to reverse engineer the battery cell design and its internal structure. The combination of inductively coupled plasma-optical emission spectrometry and incremental capacity analysis applied to three-electrode lab cells, constructed from the studied battery cell’s materials, allowed to identify the SoC ranges in which phase transitions and staging occur and thereby directly links changes in the ultrasonic signal properties with the state of the active materials, which makes this work stand out among other studies on ultrasound-based state estimation. Additional dilatometer experiments were able to prove that the measured effect in ultrasonic time of flight cannot originate from the thickness increase of the battery cells alone, as this thickness increase is smaller and in opposite direction to the change in time of flight. Therefore, changes in elastic modulus and density have to be responsible for the observed effect.
The construction of the sensor stack from off-the-shelf piezo elements, its electromagnetic shielding, and attachment to both sides of the battery cells was treated in a subsequent section. Experiments verified the necessity of shielding and its negligible influence on the ultrasonic signals. A hypothesis describing the metal layer in the pouch foil to be the transport medium of an electrical coupling/distortion between sending and receiving sensor was formulated and tested. Impedance spectroscopy was shown to be a useful tool to characterize the resonant behavior of piezo elements and ensure the mechanical coupling of such to the surface of the battery cells. The excitation of the piezo elements by a raised cosine (RCn) waveform with varied center frequency in the range of 50 kHz to 250 kHz was studied in the frequency domain and the influence of the resonant behavior, as identified prior by impedance spectroscopy, on waveform and frequency content was evaluated to be uncritical. Therefore, the forced oscillation produced by this excitation was assumed to be mechanically coupled as ultrasonic waves into the battery cells.
The ultrasonic waves transmitted through the battery cell were recorded by piezo elements on the opposing side. A first inspection of the raw, unprocessed signals identified the transmission of two main wave packages and allowed the identification of two major trends: the time of flight of ultrasonic wave packages decreases with the center frequency of the RCn waveform, and with state of charge. These trends were to be assessed further in the subsequent sections. Therefore, methods for the extraction of features (properties) from the ultrasonic signals were established, compared, and tested in a dedicated section. Several simple and advanced thresholding methods were compared with envelope-based and cross-correlation methods to estimate the time of flight (ToF). It was demonstrated that the envelope-based method yields the most robust estimate for the first and second wave package. This finding is in accordance with the literature stating that an envelope-based method is best suited for dispersive, absorptive media [204], to which lithium-ion batteries are counted. Respective trends were already suggested by the heatmap plots of the raw signals vs. RCn frequency and SoC. To enable such a robust estimate, an FIR filter had to be designed to preprocess the transmitted signals and thereby attenuate frequency components that verifiably lead to a distorted shape of the envelope.
With a robust ToF estimation method selected, the characterization of the signal properties ToF and transmitted energy content (EC) was performed in-depth. A study of cycle-to-cycle variations unveiled that the signal properties are affected by a long rest period and the associated relaxation of the multi-particle system “battery cell” to equilibrium. In detail, during cycling, the signal properties don’t reach the same value at a given SoC in two subsequent cycles if the first of the two cycles follows a long rest period. In accordance with the literature, a break-in period, making up for more than ten cycles post-formation, was observed. During this break-in period, the mechanical properties of the system are said to change until a steady state is reached [25]. Experiments at different C-rate showed that ultrasonic signal properties can sense the non-equilibrium state of a battery cell, characterized by an increasing area between charge and discharge curve of the respective signal property vs. SoC plot. This non-equilibrium state relaxes in the rest period following the discharge after the cut-off voltage is reached. The relaxation in the rest period following the charge is much smaller and shows little C-rate dependency as the state is prepared by constant voltage charging at the end of charge voltage. For a purely statistical SoC estimation approach, as employed in this work, where only instantaneous measurements are taken into account and the historic course of the measurement is not utilized as a source of information, the presence of hysteresis and relaxation leads to a reduced estimation accuracy. Future research should address this issue or even utilize the relaxation to improve the estimation accuracy, by incorporating historic information, e.g., by using the derivative of a signal property as an additional feature. The signal properties were then tested for their correlation with SoC as a function of RCn frequency. This allowed identifying trends in the behavior of the signal properties as a function of RCn frequency and C-rate in a condensed fashion and thereby enabled to predict the frequency range, about 50 kHz to 125 kHz, in which the course of the signal properties is best suited for SoC estimation.
The final section provided a proof of concept of the ultrasound-based SoC estimation, by applying a support vector regression (SVR) to before thoroughly studied ultrasonic signal properties, as well as current and battery cell voltage. The included case study was split into different parts that assessed the ability of an SVR to estimate the SoC in a variety of scenarios. Seven battery cells, prepared with sensor stacks attached to both faces, were used to generate 14 datasets. First, a comparison of self-tests, where a portion of a dataset is used for training and another for testing, and cross-tests, which use the dataset of one cell for training and the dataset of another for testing, was performed. A root mean square error (RMSE) of 3.9% to 4.8% SoC and 3.6% to 10.0% SoC was achieved, respectively. In general, it was observed that the SVR is prone to overestimation at low SoCs and underestimation at high SoCs, which was attributed to the pronounced hysteresis and relaxation of the ultrasonic signal properties in this SoC ranges. The fact that higher accuracy is achieved, if the exact cell is known to the model, indicates that a variation between cells exists. This variation between cells can originate from differences in mechanical properties as a result of production variations or from differences in manual sensor placement, mechanical coupling, or resonant behavior of the ultrasonic sensors. To mitigate the effect of the cell-to-cell variations, a test was performed, where the datasets of six out of the seven cells were combined as training data, and the dataset of the seventh cell was used for testing. This reduced the spread of the RMSE from (3.6 - 10.0)% SoC to (5.9 – 8.5)% SoC, respectively, once again stating that a databased approach for state estimation becomes more reliable with a large data basis. Utilizing self-tests on seven datasets, the effect of additional features on the state estimation result was tested. The involvement of an additional feature did not necessarily improve the estimation accuracy, but it was shown that a combination of ultrasonic and electrical features is superior to the training with these features alone. To test the ability of the model to estimate the SoC in unknown cycling conditions, a test was performed where the C-rate of the test dataset was not included in the training data. The result suggests that for practical applications it might be sufficient to perform training with the boundary of the use cases in a controlled laboratory environment to handle the estimation in a broad spectrum of use cases.
In comparison with literature, this study stands out by utilizing and modifying off-the-shelf piezo elements to equip state-of-the-art lithium-ion battery cells with ultrasonic sensors, employing a range of center frequencies for the waveform, transmitted through the battery cell, instead of a fixed frequency and by allowing the SVR to choose the frequency that yields the best result. The characterization of the ultrasonic signal properties as a function of RCn frequency and SoC and the assignment of characteristic changes in the signal properties to electrochemical processes, such as phase transitions and staging, makes this work unique. By studying a range of use cases, it was demonstrated that an improved SoC estimation accuracy can be achieved with the aid of ultrasonic measurements – thanks to the correlation of the mechanical properties of the battery cells with the SoC.
Im Rahmen der vorliegenden Arbeit wurde ein neuer Beschichtungstyp für die Elektrodenmaterialien von Lithium-Ionen-Akkumulatoren entwickelt und charakterisiert. Dieser besteht aus einem speziellen anorganisch-organischen Hybridpolymer, das sich bezüglich seiner Zusammensetzung und Funktion gegenüber bestehenden Beschichtungsmaterialien abhebt. Das anorganisch-organische Netzwerk des Hybridpolymers konnte mittels Feststoff-NMR-Messungen vollständig aufgeklärt werden. Dabei zeigte sich ein stabiles anorganisches Gerüst aus hoch vernetzten Polysiloxan-Einheiten. Zusätzliche organische Modifizierungen liegen als lange bewegliche Ketten mit funktionellen Polyethylenoxid-Einheiten vor oder sind in Form von Polyethern und Diolen vernetzt. Mit dieser speziellen Netzwerkstruktur ist es möglich, Materialeigenschaften zu erzeugen, die über solche von rein anorganischen und rein organischen Beschichtungen hinausgehen. Zu den mit verschiedenen Methoden nachgewiesenen Eigenschaften zählen eine hohe ionische Leitfähigkeit von 10\(^{-4}\) S/cm, eine hohe Elastizität mit E = 63 kPa, eine hohe elektrochemische Stabilität bis 5,0 V vs. Li/Li\(^+\) und eine hohe thermische Stabilität.
Eine weitere Besonderheit des neuen Beschichtungsmaterials ist die mehrstufige Vernetzung der anfänglichen Prekursoren zu einem Hybridpolymer-Sol und dem abschließenden Hybridpolymer-Gel. Die im Beschichtungssol vorliegende Teilvernetzung der Vorstufen konnte detailliert mittels Flüssig-NMR-Messungen untersucht und beschrieben werden. Aus den Messungen ließ sich folgern, dass die organisch und anorganisch vernetzbaren Gruppen im Sol teilweise vernetzt vorliegen. Die sterisch erreichbaren Si-OR-Gruppen der so entstandenen Oligomere sind vorwiegend nicht hydrolysiert, wodurch deren anorganische Anbindung an die OH-Gruppen der Partikeloberflächen kinetisch bevorzugt ist. Damit lassen sich besonders homogene und vollständig bedeckende Beschichtungen der Elektrodenmaterialien erzeugen. Dies konnte mit verschiedenen physikalischen und chemischen Methoden nachgewiesen werden: simulationsgestützte Rückstreuanalysen mittels REM, hochaufgelöste TEM-Aufnahmen sowie Elementanalysen durch EDX und XPS.
Nach der Optimierung des nasschemischen Beschichtungsprozesses über Rotationsverdampfen ergaben sich für die verschiedenen Elektrodenmaterialien Li\(_4\)Ti\(_5\)O\(_{12}\), Li(Ni,Co,Mn)O\(_2\) und Li(Mn,Ni)\(_2\)O\(_4\) jeweils etwa 20 nm dicke Beschichtungen mit Hybridpolymer. Die Frage nach deren Lösungsmittelbeständigkeit konnte durch die Analyse von behandelten Proben mit TG, REM, XPS und ICP-OES aufgeklärt werden. Dabei zeigte sich sowohl für die Behandlung mit NMP, dem klassischen Lösungsmittel bei der Elektrodenfertigung mit PVDF-Binder, als auch für die Behandlung mit dessen umweltschonenderem Ersatzstoff Aceton eine gute Beständigkeit der Beschichtung. Die Beschichtung löste sich in den Lösungsmitteln an, blieb allerdings als geschlossene nanoskalige Beschichtung erhalten. Lediglich gegenüber dem Lösungsmittel H\(_2\)O, das in Kombination mit dem neuen Binder CMC eingesetzt wird, wurde eine mangelnde Schichtstabilität deutlich. Das dafür verantwortliche Quellverhalten der Beschichtung konnte mittels Dünnschicht-Modellsystem und daran durchgeführten REM-, IR- und EPA-Untersuchungen aufgeklärt werden. Die Optimierung des Hybridpolymer-Materials bezüglich einer besseren H\(_2\)O-Beständigkeit übersteigt den Rahmen dieser Arbeit und liefert die Grundlage für weitere künftige Forschungsarbeiten.
Aufgrund der vollständigen Bedeckung der neuen Beschichtung, ihrer besonderen Eigenschaften und ihrer Beständigkeit bei der klassischen Elektrodenfertigung ist es möglich, die Elektrodenmaterialien grundlegend hinsichtlich ihrer wichtigsten Eigenschaften zu verbessern. Hierfür wurden sowohl über die NMP- als auch über die Aceton-Route Elektroden gefertigt und zu Halbzellen und Vollzellen verarbeitet. Die REM-Analyse der Elektroden zeigte, dass die Partikelbeschichtungen keinen negativen Einfluss auf die Homogenität und Morphologie der Elektroden ausüben. Damit war es möglich, jeweils einen direkten Vergleich von beschichteten und unbeschichteten Materialien hinsichtlich ihrer elektrochemischen Performance anzustellen. Für die Kathodenmaterialien Li(Ni,Co,Mn)O\(_2\) und Li(Mn,Ni)\(_2\)O\(_4\) ergaben die Zyklenfestigkeits- und Impedanzmessungen klare Verbesserungen durch die Beschichtung. Verbunden mit einer Verbesserung der Energiedichte erhöhte sich bei beiden Materialien die Zyklenfestigkeit um mehr als 60 %. Bei Li(Mn,Ni)\(_2\)O\(_4\) zeigt sich die Verbesserung in einer erhöhten Zellspannung durch das vergleichsweise hohe Redoxpotential des Materials von etwa 4,7 V vs. Li/Li\(^+\), während sich bei Li(Ni,Co,Mn)O\(_2\) die Hochvoltfähigkeit des Materials verbessert, was mit einer vergrößerten Speicherkapazität verbunden ist. Dabei ist herauszustellen, dass für keines der Materialien ein negativer Einfluss der dünnen Beschichtung auf die Leistungsdichte festgestellt werden konnte.
Der erwartete Mechanismus für die verbesserte Elektrodenfunktion durch das Hybridpolymer ist die Bildung einer physikalischen Schutzschicht in Form einer Li\(^+\)-leitfähigen Membran. Diese umgibt das Elektrodenmaterial vollständig, ermöglicht die Ladungsträgerinterkalation und schützt die Elektrode gleichzeitig vor irreversiblen Reaktionen mit dem Elektrolyten. Damit verbunden ist eine verminderte Mn-Auslösung und eine verminderte Entwicklung von isolierenden Deckschichten aus Reaktionsprodukten wie LiF, Li\(_2\)O, Li\(_2\)CO\(_3\), was sich positiv auf die Alterung der Batteriezellen auswirkt. Die Funktion der Beschichtung wurde primär auf den Kathodenmaterialien demonstriert. Doch auch auf der Anodenseite wurde ihre Anwendungstauglichkeit aufgezeigt, was das große Potential der Beschichtung für eine breite Anwendung in Lithium-Ionen-Batterien verdeutlicht.