The mathematical analysis has been developed by using finite volume method, experimental data from literatures, and solving numerically to predict solid oxide fuel cell performances with different operating conditions and different material properties. The in-house program presents flow fields, temperature distributions, and performance predictions of typical solid oxide fuel cells operating at different temperatures, 1000 C, 800 C, 600 C, and 500 C, and different electrolyte materials, Yttria-Stabilized zirconia (YSZ) and Gadolinia-doped ceria (CGO). From performance predictions show that the performance of an anode-supported planar SOFC is better than that of an electrolyte-supported planar SOFC for the same material used, same electrode electrochemical considerations, and same operating conditions. The anode-supported solid oxide fuel cells can be used to give the high power density in the higher current density range than the electrolyte-supported solid oxide fuel cells. Even though the electrolyte-supported solid oxide fuel cells give the lower power density and can operate in the lower current density range but they can be used as a small power generator which is portable and provide low power. Furthermore, it is shown that the effect of the electrolyte materials plays important roles to the performance predictions. This should be noted that performance comparisons are obtained by using the same electrode materials. The YSZ-electrolyte solid oxide fuel cells in this work show higher performance than the CGO-electrolyte solid oxide fuel cells when SOFCs operate above 756 C. On the other hand, when CGO based SOFCs operate under 756 C, they shows higher performance than YSZ based SOFCs because the conductivity values of CGO are higher than that of YSZ temperatures lower than 756 C. Since the CGO conductivity in this work is high and the effects of different electrode materials, they can be implied that conductivity values of electrolyte and electrode materials have to be improved.

With looming energy crisis across the globe, achieving high efficiency and low cost solar cells have long been the key objective for photovoltaic researchers. III-V compound semiconductor based multijunction solar cells have been the dominant choice for space power due to their superior performance compared to any other existing solar cell technologies. In spite of unmatched performance of III-V solar cells, Si cells have dominated the terrestrial market due to their lower cost. Most of the current III-V solar cells are grown on Ge or GaAs substrates, which are not only smaller in diameter, but are also more expensive than Si substrate. Direct integration of high efficiency III-V solar cells on larger diameter, cheaper and readily available Si substrate is highly desirable for increased density, low-cost and lightweight photovoltaics. However, the polar-on-nonpolar epitaxy, the thermal mismatch and the 4% lattice mismatch makes the direct growth of GaAs on Si challenging, rendering the metamorphic cell sensitive to dislocations. The focus of this work is to investigate and correlate the impact of threading dislocation density on the performance of lattice-mismatched single-junction (1J) GaAs and dual-junction (2J) InGaP/GaAs solar cells on Si substrate. Utilizing our calibrated dislocation-assisted modeling process, we present the design methodology to optimize the structure of 2J InGaP/GaAs solar cell on Si substrate. Our modeling results suggest an optimistic future for integrating III-V solar cell technology on Si substrate and will be useful for future design and prediction of metamorphic III-V solar cell performance on Si substrate. / Master of Science

This thesis is an investigation of the anode of a direct methanol fuel cell (DMFC) through numerical modeling and simulation. This model attempts to help better understand the two phase flow phenomena in the anode as well as to explain some of the many problems on the anode side of a DMFC and show how changing some of the anode side properties could alleviate these problems. This type of modeling is important for designing and optimizing the DMFC for specific applications like portable electronics. Understanding the losses within the DMFC like removable of carbon dioxide, conversion losses, and methanol crossover from the anode to the cathode will help the DMFC become more commercially viable. The model is based on two phase flow in porous media combined with equilibrium between phases in a porous media with contributions from a capillary pressure difference. The effect of the physical parameters of the fuel cell like the thickness, permeability, and contact angle as well as the operating conditions like the temperature and methanol feed concentration, have on the performance of the DMFC during operation will be investigated. This will show how to remove the gas phase from the anode while enabling methanol to reach the catalyst layer and minimizing methanol crossover. / text

Mathematical modeling has been instrumental to the development of natural sciences over the last half-century. Through iterated interactions between modeling and real-world exper- imentation, these models have furthered our understanding of the processes in biology and chemistry that they seek to represent. In certain application domains, such as the field of car- diac biology, communities of modelers with common interests have emerged, leading to the development of many models that attempt to explain the same or similar phenomena. As these communities have developed, however, reporting standards for modeling studies have been in- consistent, often focusing on the final parameterized result, and obscuring the assumptions and data used during their creation. These practices make it difficult for researchers to adapt exist- ing models to new systems or newly available data, and also to assess the identifiability of said models - the degree to which their optimal parameters are constrained by data - which is a key step in building trust that their formulation captures truth about the system of study. In this thesis, we develop tools that allow modelers working with biological or chemical time series data to assess identifiability in an automated fashion, and embed these tools within a novel online community resource that enforces reproducible standards of reporting and facilitates exchange of models and data. We begin by exploring the application of Bayesian and approximate Bayesian inference methods, which parameterize models while simultaneously assessing uncertainty about these estimates, to assess the identifiability of models of the cardiac action potential. We then demon- strate how the side-by-side application of these Bayesian and approximate Bayesian methods can be used to assess the information content of experiments where system observability is limited to "summary statistics" - low-dimensional representations of full time-series data. We next investigate how a posteriori methods of identifiability assessment, such as the above inference techniques, compare against a priori methods based on model structure. We compare these two approaches over a range of biologically relevant experimental conditions, and high- light the cases under which each strategy is preferable. We also explore the concept of optimal experimental design, in which measurements are chosen in order to maximize model identifia- bility, and compare the feasibility of established a priori approaches against a novel a posteriori approach. Finally, we propose a framework for representing and executing modeling experiments in a reproducible manner, and use this as the foundation for a prototype "Modeling Web Lab" where researchers may upload specifications for and share the results of the types of inference explored in this thesis. We demonstrate the Modeling Web Lab's utility across multiple mod- eling domains by re-creating the results of a contemporary modeling study of the hERG ion channel model, as well as the results of an original study of electrochemical redox reactions. We hope that this works serves to highlight the importance of both reproducible standards of model reporting, as well as identifiability assessment, which are inherently linked by the desire to foster trust in community-developed models in disciplines across the natural sciences.

Electrode microstructure directly affects ion and electron transport and, in turn, has a strong correlation to battery performance. Understanding the separate yet complementary effects of ionic and electronic transport in cell behavior is a challenge. This work provides through a combination of experiments and modeling a better understanding of the relationship between three aspects of the cell: ion transport within the electrode, electrode uniformity, and cell degradation. The first part of this work compares two experimental methods that determine ion transport in terms of tortuosity, a dimensionless geometric factor. The polarization-interrupt and blocking-electrolyte methods measure effective diffusivity and conductivity, respectively. The tortuosity of several commercial-quality electrodes was measured using both methods, producing reasonable agreement between the two methods in most cases. Next, the effect of cell cycling on ionic and electronic transport of electrodes was investigated. Using the blocking electrolyte method, the tortuosity of electrode films at varying extents of cycling was determined. Variations in electronic resistivity were quantified by micro-scale measurements using a previously developed micro-four-line probe. The changes in tortuosity and electronic resistivity were investigated for a graphite anode and several cathode chemistries including LiCoO2, LiNixCoyMnzO2, LiFePO4, and blends of transition metal oxides. Clear evidence of changes in tortuosity and electronic resistivity was observed during cell formation and cycling. The magnitude of the changes strongly depended on the chemistry of electrodes and cycling conditions. The results indicate that, under normal cycling conditions, electronic resistivity increases while tortuosity unexpectedly decreases. However, accelerated cycling conditions (i.e. elevated temperature) can lead to both electronic resistivity and tortuosity increase. Finally, the interplay of electrode tortuosity heterogeneity and Li-plating was investigated. The Li-plating reaction was incorporated into a Newman-type model and validated using the voltage profile and capacity-loss data from experiments. The simulation result shows that a heterogeneous anode can cause non-uniform Li plating while cathode heterogeneity did not have a significant effect. The Li-plating profile across the thickness of the anode with cell cycling showed that Li tends to plate at the high tortuosity region near the separator. Unexpectedly, Li plating tends to shift to the current collector side upon a sufficient increase in porosity close to the separator. Simulated capacity loss vs. cycling data indicates that there is a feedback mechanism with cycling: as cycling continues the rate of Li plating for the high-tortuosity region decreases at the separator side and the other two regions will eventually catch up in terms of plating.

Lithium-ion batteries are critical components in electric vehicles, portable electronics, and grid energy storage systems, necessitating advanced modeling techniques to enhance their safety, performance, and lifespan. This thesis presents the development and validation of a coupled electrical and lumped thermal model for cylindrical lithium-ion batteries along with a finite difference thermal model for spatial temperature prediction of cylindrical cell These models address key challenges in simulating real-world battery behavior. The electrical model utilizes a 2 R-C pair equivalent circuit framework integrated with a busbar model to account for current imbalances in parallel-connected cells. This model is a common equivalent circuit model used to represent a Li-ion cell using a voltage source, series resistor, and two resistor-capacitor pair connected in parallel. A lumped thermal model coupled with the electrical framework dynamically adjusts parameters based on temperature variations, achieving a voltage prediction error of less than 200 mV. Additionally, the thermal model employs a finite difference method (FDM) to solve the 3D transient heat conduction equation, providing spatial temperature distribution within cells and capturing critical gradients between core and surface temperatures. The vectorization of the thermal solver reduced simulation time by half, and its validation against Ansys™ simulations and module-level data demonstrated temperature prediction accuracy within a 2–3°C margin. The developed tool is scalable for any number of cylindrical cells arranged in a rectangular grid, addressing key gaps identified in the literature, including the need to simulate spatial and temporal non-uniformities in state-of-charge (SOC), state-of-health (SOH), and temperature, which significantly affect battery performance and lifespan. It provides a scalable, efficient tool for predicting thermal and electrical behavior across cell and module levels. This work contributes to the development of a tool that will, enable informed design decisions for next-generation energy storage systems. Future research could focus on extending the model to incorporate aging effects, enhanced thermal management configurations, and real-time simulations for battery management systems. / Master of Science / Lithium-ion batteries play a crucial role in powering electric vehicles, smartphones, and renewable energy storage systems. As demand for these technologies grows, ensuring that batteries operate safely and efficiently becomes increasingly important. This research focuses on developing computer models that simulate how lithium-ion batteries behave under different conditions, helping engineers design better and longer-lasting batteries. The project introduces two main models: an electrical model that predicts how energy flows through a battery and a thermal model that estimates how the battery heats up during use. The electrical model simplifies complex battery behavior by representing it with basic circuit components, while the thermal model uses advanced calculations to simulate how heat spreads within the battery. By combining these models, the research creates a tool that can predict how batteries perform over time and how temperature changes affect their efficiency and lifespan. One of the key achievements of this work is improving the speed and accuracy of these simulations. The thermal model was enhanced to calculate heat distribution more efficiently, cutting simulation times in half. The model was also validated against industry-standard tools like Ansys™, with results showing temperature predictions within a 2-3°C margin of error. This tool can simulate battery packs of any size, making it valuable for designing electric vehicle batteries and large-scale energy storage systems. By identifying potential issues like overheating or uneven energy distribution, the model helps engineers develop safer and more reliable battery technologies. Ultimately, this research contributes to the advancement of energy storage systems, supporting the transition to cleaner and more sustainable energy solutions for the future.

Achieving high efficiency solar cells and concurrently driving down the cell cost has been among the key objectives for photovoltaic researchers to attain a lower levelized cost of energy (LCOE). While the performance of silicon (Si) based solar cells have almost saturated at an efficiency of ~25%, III-V compound semiconductor based solar cells have steadily shown performance improvement at approximately 1% (absolute) increase per year, with a recent record efficiency of 46%. However, the expensive cost has made it challenging for the high efficiency III-V solar cells to compete with the mainstream Si technology. Novel approaches to lower down the cost per watt for III-V solar cells will position them to be among the key contenders in the renewable energy sector. Integration of such high-efficiency III-V multijunction solar cells on significantly cheaper and large area Si substrate has the potential to address the future LCOE roadmaps by unifying the high-efficiency merits of III-V materials with low-cost and abundance of Si. However, the 4% lattice mismatch, thermal mismatch polar-on-nonpolar epitaxy makes the direct growth of GaAs on Si challenging, rendering the metamorphic cell sensitive to dislocations. The focus of this dissertation is to systematically investigate heterogeneously integrated III-V multijunction solar cells on Si substrate. Utilizing a combination of comprehensive solar cell modeling and experimental techniques, we seek to better understand the material properties and correlate them to improve the device performance, with simulation providing a very valuable feedback loop. Key technical design considerations and optimal performance projections are discussed for integrating metamorphic III-V multijunction solar cells on Si substrates for 1-sun and concentrated photovoltaics. Key factors limiting the “GaAs-on-Si” cell performance are identified, and novel approaches focused on minimizing threading dislocation density are discussed. Finally, we discuss a novel epitaxial growth path utilizing high-quality and thin epitaxial Ge layers directly grown on Si substrate to create virtual “Ge-on-Si” substrate for III-V-on-Si multijunction photovoltaics. With the plummeting price of Si solar cells accompanied with the tremendous headroom available for improving the III-V solar cell efficiencies, the future prospects for successful integration of III-V solar cell technology with Si substrate looks very promising to unlock an era of next generation of high-efficiency and low-cost photovoltaics. / Ph. D.

Solid oxide fuel cells (SOFCs) are high temperature (600C-1000C) composite metallic/ceramic-cermet electrochemical devices. There is a need to effectively manage the heat transfer through the cell to mitigate material failure induced by thermal stresses while yet preserving performance. The present dissertation offers a novel thermodynamic optimization approach that utilizes dimensionless geometric parameters to design a SOFC. Through entropy generation minimization, the architecture of a planar SOFC has been redesigned to optimally balance thermal gradients and cell performance. Cell performance has been defined using the 2nd law metric of exergetic efficiency. One constrained optimization problem was solved. The optimization sought to maximize exergetic efficiency through minimizing total entropy production while constraining thermal gradients. Optimal designs were produced that had exergetic efficiency exceeding 92% while maximum thermal gradients were between 219 C/m and 1249 C/m. As the architecture was modified, the magnitude of sources of entropy generation changed. Ultimately, it was shown that the architecture of a SOFC can be modified through thermodynamic optimization to maximize performance while limiting thermal gradients. The present dissertation highlights a new design methodology and provides insights on the connection between thermal gradients, performance, sources of entropy generation, and cell architecture.

This dissertation reports on a new methodology to characterize and simulate a standard cell library to be used for statistical static timing analysis. A compact variation-aware timing model for a standard cell in a cell library has been developed. The model incorporates variations in the input waveform and loading, process parameters, and the environment into the cell timing model. Principal component analysis (PCA) has been used to form a compact model of a set of waveforms impacted by these sources of variation. Cell characterization involves determining equations describing how waveforms are transformed by a cell as a function of the input waveforms, process parameters, and the environment. Different versions of factorial designs and Latin hypercube sampling have been explored to model cells, and their complexity and accuracy have been compared. The models have been evaluated by calculating the delay of paths. The results demonstrate improved accuracy in comparison with table-based static timing analysis at comparable computational cost. Our methodology has been expanded to adapt to interconnect dominant circuits by including a resistive-capacitive load model. The results show the feasibility of using the new load model in our methodology. We have explored comprehensive accuracy improvement methods to tune the methodology for the best possible results. The following is a summary of the main contributions of this work to the statistical static timing analysis: (a) accurate waveform modeling for standard cells using statistical waveform models based on principal components; (b) compact performance modeling of standard cells using experimental design statistical techniques; and (c) variation-aware performance modeling of standard cells considering the effect of variation parameters on performance, where variation parameters include loading, waveform shape, process parameters (gate length and threshold voltage of NMOS and PMOS transistors), and environmental parameters (supply voltage and temperature); and (f) extending our methodology to support resistive-capacitive loads to be applicable to interconnect dominant circuits; and (e) classifying the sources of error for our variational waveform model and cell models and introducing of the related accuracy improvement methods; and (f) introducing our fast block-based variation-aware statistical dynamic timing analysis framework and showing that (i) using compiler-compiler techniques, we can generate our timing models, test benches, and data analysis for each circuit, which are compiled to machine-code to reduce the overhead of dynamic timing simulation, and (ii) using the simulation engine, we can perform statistical timing analysis to measure the performance distribution of a circuit using a high-level model for gate delay changes, which can be linked to their parameter variation.

The energy crisis and environmental pollution have become increasingly prominent in recent years. Lithium batteries have attracted extensive attention due to their high energy density, safety, and low pollution. To further study how the battery works, it is necessary to establish an accurate model conforming to the battery characteristics. As the core function of a battery management system(BMS), accurate state of charge(SoC) estimation dramatically improves battery life and performance. This thesis selects a ternary lithium battery in the centre for advanced life cycle engineering(CALCE) dataset for a study of cell modeling and SoC estimation. The second-order Thevenin equivalent circuit model is selected as the cell model due to a trade-off between model complexity and accuracy. The parameters to identify include OCV, internal ohmic resistance, polarized internal resistance and capacitance. They were obtained with the MATLAB toolbox at various SoC state points under different temperatures. The ‘terminal voltage comparison’ method is utilized to verify the identification's accuracy. The simulation results turn out to be satisfactory. Then cell SoC can be estimated after cell modeling. First, the principles of the Coulomb counting method, OCV method and EKF method are analyzed. The state space equations required in SoC estimation are determined by discretizing the non-linear equivalent circuit model. The simulation results are compared with the experimental results in the HPPC discharge experiment. Furthermore, the robustness of the EKF algorithm is further investigated. The results prove that the EKF algorithm has high precision, fast convergence speed and strong anti-interference capability. Last but not least, the research on battery pack SoC estimation was continued. How to expand a single cell into a battery pack is analyzed, including aggregating cells into a pack and scaling a cell model to a pack. In addition, battery pack SoC is individually estimated by the 'Big cell' method and 'Short board effect' method. The result is not so good, indicating that further work can be done to improve the SoC estimation accuracy. / Energikrisen och miljöföroreningarna har blivit allt mer framträdande de senaste åren. Litiumbatteri har väckt stor uppmärksamhet på grund av sin höga energitäthet, säkerhet och låga föroreningar. För att ytterligare studera hur batteriet fungerar är det nödvändigt att etablera en exakt modell som överensstämmer med batteriets egenskaper. Som kärnfunktionen hos BMS förbättrar noggrann SoC-uppskattning dramatiskt batteriets livslängd och prestanda. Denna avhandling väljer ett ternärt litiumbatteri i CALCE-datauppsättningen för forskning. Dessutom slutförs cellmodellering och SoC-uppskattning baserat på det. Den andra ordningens Thevenins ekvivalenta kretsmodell väljs som cellmodell på grund av en avvägning mellan modellens komplexitet och noggrannhet. Parametrarna som måste identifieras inkluderar OCV, intern ohmsk resistans, polariserad intern resistans och kapacitans. De erhölls med MATLAB-verktygslådan vid olika SoC-tillståndspunkter under olika temperaturer. Metoden "terminalspänningsjämförelse" används för att verifiera identifieringens noggrannhet. Simuleringsresultaten visar sig vara tillfredsställande. Sedan kan cell SoC uppskattas efter cellmodellering. Först analyseras principerna för Coulomb-räknemetoden, OCV-metoden och EKF-metoden. Tillståndsrymdsekvationerna som krävs vid SoC-uppskattning bestäms genom att diskretisera den icke-linjära ekvivalenta kretsmodellen. Simuleringsresultaten jämförs med de experimentella resultaten i HPPC-utsläppsexperimentet. Dessutom, robustheten hos EKF-algoritmen undersöks ytterligare. Resultaten bevisar att EKF-algoritmen har hög precision, snabb konvergenshastighet och stark anti-interferensförmåga. Sist men inte minst fortsatte forskningen kring SoC-uppskattning av batteripaket. Hur man expanderar ett enskilt batteri till ett batteripaket analyseras, inklusive aggregering av celler till ett paket och skalning av en cellmodell till ett paket. Dessutom uppskattas batteripaketets SoC individuellt med "Big cell"-metoden och "Short board effect"-metoden. Resultatet är inte så bra, vilket indikerar att ytterligare arbete kan göras för att förbättra SoC-uppskattningens noggrannhet.