<p>The single particle model was extended to include electrode and particle volume expansion effects observed in high capacity alloying electrodes. The model was used to predict voltage profiles in sodium ion batteries with tin and tin-phosphide negative electrodes. It was seen that the profiles predicted by the modified model were significantly better than the classical model. A parametric study was done to understand the impact of properties such as particle radius, diffusivity, reaction rate etc on the performance of the electrode. The model was also modified for incorporating particles having a cylindrical morphology. For the same material properties, it was seen that cylindrical particles outperform spherical particles for large L/R values in the cylinder due to the diffusion limitations at low L/R ratios. A lattice spring-based degradation model was used to observe crack formation and creep relaxation within the particle. It was observed that the fraction of broken bonds increases with an increase in strain rate. At low strain rates, it was seen that there was a significant expansion in particle volumes due to creep deformation. This expansion helped release particle stresses subsequently reducing the amount of fracture.</p>

This thesis investigates novel algorithms for enabling the use of first-principle electrochemical models for battery monitoring and control in advanced battery management systems (BMSs). Specifically, the fast solution and state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional (P2D) model are investigated. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the P2D model is then used in combination with an extended Kalman filter (EKF) algorithm modified for differential-algebraic equations (DAEs) to estimate the states of the model, e.g. lithium concentrations, overpotential. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200s despite a 30% error on battery initial state-of-charge (SoC) and additive measurement noise with 10mV and 0.5&deg;C standard deviations. The parameter accuracy of such first-principle models is of utmost importance for the trustworthy estimation of internal battery electrochemical states. Therefore, the identifiability of the simpler single particle (SP) electrochemical model is investigated both in principle and in practice. Grouping parameters and partially non-dimensionalising the SP model equations in order to understand the maximum expected degrees of freedom in the problem reveals that there are only six unique parameters in the SP model. The structural identifiability is then examined by asking whether the transfer function of the linearised SP model is unique. It is found that the model is unique provided that the electrode open circuit voltage curves have a non-zero gradient, the parameters are ordered, and that the behaviour of the kinetics of each electrode is lumped together into a single parameter which is the charge transfer resistance. The practical estimation of the SP model parameters from frequency-domain experimental data obtained by electrochemical impedance spectroscopy (EIS) is then investigated and shows that estimation at a single SoC is insufficient to obtain satisfactory results and EIS data at multiple SoCs must be combined.

Batterimodeller används för att representera batterier. För ändamål som batterihanteringssystem används idag främst empiriska modeller som representerar ett batteri med en motsvarande kretsmodell. Några nackdelar för dessa modeller ligger i dess oförmåga att simulera interna tillstånd och en tidskrävande parametriseringsprocess. Dessa nackdelar motiverar ingenjörer att vända sig till modeller som är baserade på fysiska lagar som ett alternativ eftersom de kan ge insikt i vad som händer inuti batteriet. Batterimodellerna som är baserade på de fysiska lagarna har alltför krävande beräkningar för att kunna användas för vissa applikationer, som batterihanteringssystem. Singel-partikelmodellen (SPM) är en fysikbaserad modell som används i detta avhandlingsprojekt. Syftet med projektet var att hitta en metod för att parametrisera SPM för nya kommersiella cylindriska HTPFR18650 1100mAh 3.2V litiumjärnfosfatceller. En litteraturundersökning och experiment användes för att extrahera parametervärdena. 17 parametrar valdes från litteraturundersökningen eftersom de kunde användas för att parametrisera modellen. Geometriska parametrar hittades genom en cellöppning. Tre typer av icke-destruktiva experiment som var inspirerade av litteraturen utfördes för att extrahera värden för de andra icke-geometriska parametrarna. Ett cykeltest med låg strömhastighet utfördes för att få en pseudo-OCV-kurva och för att extrahera kapacitetsrelaterade parametrarna. En känslighetsanalys genomfördes för galvanostatisk intermittent titreringsteknik testet (GITT) och pulstestet för de parametrar som var kopplade till transportoch kinetiska fenomen. Python matematisk batterimodellering (PyBaMM) användes för att simulera experimenten. Parametersamlingen Prada 2013 användes som standardvärden. Standardvärdena för de valda parametrarna ersattes av de värden som hittades genom experiment. Känslighetsanalysen visade att några av de valda parametrarna var känsliga för experimenten medan andra inte var det. Parametrarna extraherades genom fysiska relationer och genom att anpassa parametervärde för simuleringen så att den passar den experimentella datan under urladdningsförloppet. Värden för 14 av de 17 parametrarna extraherades i metoden. Den parametriserade modellen validerades mot två potentiella applikationer, en för ett batterielfordon och den andra för ett mild-hybridfordon. Den parametriserade modellen visade att den negativa partikelradien inte kan hittas med den föreslagna parametriseringsmetoden. Simuleringen visade sig också matchade den experimentella datan bättre under urladdning av cellerna jämfört till uppladdning. Flera förbättringar för framtida arbete har föreslagits, såsom att utvidgning av känslighetsanalysen, att erhålla OCV-kurvan från GITT istället för att använda pseudo-OCVkurvan, att använda strängare gränser vid kurvanpassningarna samt att skapa mer optimala tester för att extrahera parametervärdena. / Battery models are used to represent batteries. For purposes like battery management systems, empirical based models like the equivalent circuit models are widely used. These models have downsides regarding for example inability to simulate internal states and parametrization time that make engineers look at physics-based models as an alternative. The physics-based models are made up of physical relationships that offer insights into what is happening inside the battery. These are too computationally demanding to be used for certain applications, like battery managements systems. The Single Particle Model (SPM) is a physics-based model that is utilized in this thesis project. The aim of the project is to find a method to parametrize the SPM for fresh commercial cylindrical HTPFR18650 1100mAh 3.2V lithium iron phosphate cells. Literature survey and experiments were used to extract the parameter values. 17 parameters were selected from the literature survey since they could be used to parametrize the model. Geometrical parameters were found through a cell opening. Three types of nondestructive experiments inspired by literature were performed to extract values for the other non-geometric parameters. A low-rate cycling test was performed to get pseudo-OCV curve and to extract capacity related parameters. A sensitivity analysis is done for the GITT and the Pulse test for the parameters that were connected to the transport and kinetic phenomena. Python mathematical battery modelling (PyBaMM) was used to simulate the experiments. The Prada 2013 parameter set was be used as default values. The default values for the selected parameters were replaced by the values found through experiments. The sensitivity analysis showed that some of the selected parameters were sensitive while others were not. The parameters were extracted through physical relations and through curve fitting procedures during discharge. Values for 14 out of the 17 parameters were extracted in the method. The parametrized model was validated against two potential applications, one for a battery electric vehicle and the other for a mild hybrid. The parametrized model showed that the negative particle radius cannot be found through the proposed parametrization procedure. The simulation matched the experimental data better for discharging cells than charging cells. Several improvements for future work have been suggested such as extending the sensitivity analysis, obtaining the OCV-curve from GITT instead of low-rate cycling, having stricter bounds for the curve fitting as well as creating more optimal tests to extract the parameter values.

The rate of degradation of a lithium-ion battery depends on its use i.e. how it is charged and discharged. Physics-based models are used to represent the processes inside a cell as well as the degradation mechanisms. This thesis aimed to compare how the battery lifetime is affected when charging with different charging protocols using different battery models and degradation mechanisms. The investigated models are the Single Particle Model (SPM), the Single Particle Model with electrolyte (SPMe), and the Doyle-Fuller Newman model (DFN). The degradation mechanisms are solid electrolyte interphase (SEI), and lithium plating (LP). The used charging protocols are constant-current constant voltage(CCCV), positive pulsed current (PPC), and constant current (CC). Pulsed charging was included to investigate if the battery lifetime can be improved as in an experiment by Huang where pulsed charging increased the battery lifetime by 60%. To perform the simulations using the physics-based models, PyBaMM (PythonBattery Mathematical Modeling) was used. The simulations were performed for a lithium cobalt oxide (LCO) cell. Two types of SEI were implemented, solvent-diffusion limited and reaction limited. For the LP only irreversible LP was used.1200 cycles were simulated. Comparing the PPC and CC protocols, there were no significant changes between the degradation mechanisms for the different protocols. The results were the same for all the models, except for the results of the internal resistance. The conclusion is that for the PPC and CC protocols, the cell degrades the same although the PPC protocol used twice the C-rate. The PPC charging did not increase the battery lifetime. For the CCCV and CC protocols, there were some bigger differences between the protocols, but between the different models, there weren’t any significant differences. The CCCV degrades the cell faster for all degradation mechanisms and all models. Simulating one degradation submodel at a time resulted in a very small capacity fade for some submodels. Therefore, for future work, it is suggested to use several degradation submodels at the same time but also to try other degradation mechanisms or try PPC protocols with different frequencies and duty cycles. / Hur snabbt litiumjonbatterier degraderas beror på hur de används, laddas och laddas ur. Fysikbaserde modeller används för att representera processerna inuti cellen och även degraderingsmekanismerna. Denna studie har genomförts för att undersöka hur batteriets livslängd påverkas av olika laddningsprotokoll genom att använda olika batterimodeller och degraderingsmekanismer. Modellerna som användes är Singel-partikelmodellen (SPM), Singel-partikelmodellen med elektrolyt (SPMe) och Doyle-Fuller Newman-modellen (DFN). Degraderingsmekanismerna är fast elektrolytinterfas (SEI) och litiumplätering (LP). Laddningsprotokollen som användes är konstant ström konstant spänning (CCCV), positiv pulserande ström (PPC) och konstant ström konstant (CC). Protokollet för pulsad laddning inkluderades för att undersöka om batteriets livslängd kan förbättras som i ett experiment av Huang, där pulsad laddning ökade batteriets livslängdmed 60%. För att utföra simuleringar med fysikbaserade modeller användes PyBaMM(Pyhton Battery Mathematical Modeling). Simuleringarna utfördes för en lithiumkobaltoxid-cell (LCO). Två typer av SEI implementerades, lösningsmedelsdiffusion-begränsad och reaktions-begränsad SEI. För LP användes endast irreversibel LP.1200 cykler simulerades. Jämförande PPC- och CC-protokollen fanns det inga signifikanta förändringar mellan degraderingsmekanismerna för de olika protokollen. Resultaten vardesamma för alla modellerna, förutom resultaten av den interna resistansen. Slutsatsen är att för både PPC- och CC-protokollen så degraderades cellen på samma sätt, trots att PPC-protokollet använde dubbelt så hög C-faktor. PPC-protokollet ökade inte batteriets livslängd. För CCCV- och CC-protokollen fanns det några större skillnader mellan protokollen, men mellan de olika modellerna fanns det inga signifikanta skillnader. CCCV-protokollet försämrade cellen snabbare för alla degraderingsmekanismer och alla modeller. Att simulera en degraderingsmodell i taget resulterade i mycket små kapacitetsförluster. Därmed föreslås det att i framtida arbete använda flera degraderingsmodeller samtidigt men även testa andra degraderingsmekanismer eller PPC-protokoll med olika frekvenser och arbetscykler