The viability of modified gravity theories

PhDThis thesis studies the viability of classes of modified gravity (MG) theories based on generalisations of the Einstein-Hilbert action. Particular emphasis is given to f(R) theories in both the metric and Palatini formalisms, scalar-tensor theories and generalised Gauss-Bonnet theories. An urgent task at present is to devise stringent tests in order to reduce the range of candidate models based on these theories. In this thesis a detailed study is made of the viability of these models using constraints from requirement of stability, background cosmological dynamics, local gravity constraints (LGC) and matter density perturbations. In each case the conditions required for stability and viability of the background dynamics are presented. In the case of generalised Gauss-Bonnet theories the circumstances leading to the existence and stability of cosmological scaling solutions are established. In the scalar-tensor theories considered here, which includes metric-f(R) theories as a special case, there is a strong coupling of the scalar field to matter in the Einstein frame which violates all LGC. It is shown that using a chameleon mechanism, models that are compatible with LGC may be constructed. It is found that such models, which are also consistent with background dynamics, are constrained to be close to the CDMmodel during the radiation/matter epochs and can lead to the divergence of the equation of state of dark energy. In contrast, such constraints only impose mild restrictions on Palatini-f(R) models. Still more stringent constraints are provided by studying matter density perturbations. In particular, it is shown that the unconventional evolution of perturbations in the Palatini formalism leads to f(R) models in this case to be practically identical to the CDM model. For each case it is also shown that (for viable models) matter perturbation equations derived under a sub-horizon approximation are reliable even for super-Hubble scales provided the oscillating mode does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism, where the oscillating mode is absent. In summary, the analyses carried out in this thesis suggest that subjectingMG theories to observational constraints confines the viable range of models to be very close to (and in some cases indistinguishable from) the CDM model

The effects of high frequency current ripple on electric vehicle battery performance

The power electronic subsystems within electric vehicle (EV) powertrains are required to manage both the energy flows within the vehicle and the delivery of torque by the electrical machine. Such systems are known to generate undesired electrical noise on the high voltage bus. High frequency current oscillations, or ripple, if unhindered will enter the vehicle’s battery system. Real-world measurements of the current on the high voltage bus of a series hybrid electric vehicle (HEV) show that significant current perturbations ranging from 10 Hz to in excess of 10 kHz are present. Little is reported within the academic literature about the potential impact on battery system performance and the rate of degradation associated with exposing the battery to coupled direct current (DC) and alternating currents (AC). This paper documents an experimental investigation that studies the long-term impact of current ripple on battery performance degradation. Initial results highlight that both capacity fade and impedance rise progressively increase as the frequency of the superimposed AC current increases. A further conclusion is that the spread of degradation for cells cycled with a coupled AC–DC signal is considerably more than for cells exercised with a traditional DC waveform. The underlying causality for this degradation is not yet understood. However, this has important implications for the battery management system (BMS). Increased variations in cell capacity and impedance will cause differential current flows and heat generation within the battery pack that if not properly managed will further reduce battery life and degrade the operation of the vehicle

Density perturbations in f(R) gravity theories in metric and Palatini formalisms

We make a detailed study of matter density perturbations in both metric and Palatini formalisms in theories whose Lagrangian density is a general function, f(R), of the Ricci scalar. We derive these equations in a number of gauges. We show that for viable models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a sub-horizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behaviour of density perturbations as well as gravitational potentials for a number of classes of theories. In the metric formalism the parameter m=Rf_{,RR}/f_{,R} characterising the deviation from the Lambda CDM model is constrained to be very small during the matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10^{-1} around the present epoch can be allowed. These models also suffer from an additional fine tuning due to the presence of scalaron modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than ~ 0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < 10^{-5} - 10^{-4}. This is due to the peculiar evolution of matter perturbations in the Palatini case which exhibits a rapid growth or a damped oscillation depending on the sign of m.Comment: 36 pages including 8 figures. Accepted for publication in Physical Review

Characterising lithium-ion battery degradation through the identification and tracking of electrochemical battery model parameters

Lithium-ion (Li-ion) batteries undergo complex electrochemical and mechanical degradation. This complexity is pronounced in applications such as electric vehicles, where highly demanding cycles of operation and varying environmental conditions lead to non-trivial interactions of ageing stress factors. This work presents the framework for an ageing diagnostic tool based on identifying and then tracking the evolution of model parameters of a fundamental electrochemistry-based battery model from non-invasive voltage/current cycling tests. In addition to understanding the underlying mechanisms for degradation, the optimisation algorithm developed in this work allows for rapid parametrisation of the pseudo-two dimensional (P2D), Doyle-Fuller-Newman, battery model. This is achieved through exploiting the embedded symbolic manipulation capabilities and global optimisation methods within MapleSim. Results are presented that highlight the significant reductions in the computational resources required for solving systems of coupled non-linear partial differential equations

Prediction of battery storage ageing and solid electrolyte interphase property estimation using an electrochemical model

Ageing prediction is often complicated due to the interdependency of ageing mechanisms. Research has highlighted that storage ageing is not linear with time. Capacity loss due to storing the battery at constant temperature can shed more light on parametrising the properties of the Solid Electrolyte Interphase (SEI); the identification of which, using an electrochemical model, is systematically addressed in this work. A new methodology is proposed where any one of the available storage ageing datasets can be used to find the property of the SEI layer. A sensitivity study is performed with different molecular mass and densities which are key parameters in modelling the thickness of the SEI deposit. The conductivity is adjusted to fine tune the rate of capacity fade to match experimental results. A correlation is fitted for the side reaction variation to capture the storage ageing in the 0%–100% SoC range. The methodology presented in this paper can be used to predict the unknown properties of the SEI layer which is difficult to measure experimentally. The simulation and experimental results show that the storage ageing model shows good accuracy for the cases at 50% and 90% and an acceptable agreement at 20% SoC

Sizing tool for rapid optimisation of pack configuration at early-stage automotive product development

The specifications that define an automotive development project are established at an early point in the process and define the direction of such a development, and changing these decisions becomes more costly the further the project progresses. Tools to enable better consideration of choice can help prevent this. The tool presented is designed to aid with the decisions needed when embarking on the development of a vehicle that incorporates electric-vehicle technologies and the important choices made regarding the battery pack required by such a vehicle. The tool incorporates a sizing model for determining the number of cells and the configuration required to meet a specified battery requirement. The tool then uses a 1-d model to determine some of the basic thermal and power characteristics that can then be used to inform other parts of the design specification. When attached to a database containing cell information, the tool can pre-select candidate cells to meet the requirement, and rapid execution time of the tool means that it can be used to quickly compare between cell choices, at a level understandable by all stakeholders in the decision making process. Document type: Conference objec

Parameter estimation of the fractional-order Hammerstein–Wiener model using simplified refined instrumental variable fractional-order continuous time

© 2017 The Authors. Published by IET. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1049/iet-cta.2017.0284This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single-input–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input–output data by considering the system to be a multi-input–single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein–Wiener output model

On the possibility of extending the lifetime of lithium-ion batteries through optimal V2G facilitated by a flexible integrated vehicle and smart-grid system

Renewable energies are a key pillar of power sector decarbonisation. Due to the variability and uncertainty they add however, there is an increased need for energy storage. This adds additional infrastructure costs to a degree that is unviable: for an optimal case of 15GW of storage by 2030, the cost of storage is circa: £1000/kW. A promising solution to this problem is to use the batteries contained within electric vehicles (EVs) equipped with bi-directional charging systems to facilitate ancillary services such as frequency regulation and load balancing through vehicle to grid (V2G) technologies. Some authors have however dismissed V2G as economically unviable claiming the cost of battery degradation is larger than arbitrage. To thoroughly address the viability of V2G technologies, in this work we develop a comprehensive battery degradation model based on long-term ageing data collected from more than fifty long-term degradation experiments on commercial C6/LiNiCoAlO2 batteries. The comprehensive model accounts for all established modes of degradation including calendar age, capacity throughput, temperature, state of charge, depth of discharge and current rate. The model is validated using six operationally diverse real-world usage cycles and shows an average maximum transient error of 4.6% in capacity loss estimates and 5.1% in resistance rise estimates for over a year of cycling. This validated, comprehensive battery ageing model has been integrated into a smart grid algorithm that is designed to minimise battery degradation. We show that an EV connected to this smart-grid system can accommodate the demand of the power network with an increased share of clean renewable energy, but more profoundly that the smart grid is able to extend the life of the EV battery beyond the case in which there is no V2G. Extensive simulation results indicate that if a daily drive cycle consumes between 21% and 38% state of charge, then discharging 40% to 8% of the batteries state of charge to the grid can reduce capacity fade by approximately 6% and power fade by 3% over a three month period. The smart-grid optimisation was used to investigate a case study of the electricity demand for a representative University office building. Results suggest that the smart-grid formulation is able to reduce the EVs’ battery pack capacity fade by up to 9.1% and power fade by up to 12.1%

A comparison of methodologies for the non-invasive characterisation of commercial Li-ion cells

Lithium-ion cells currently power almost all electronic devices and power tools; they are a key enabling technology for electric vehicles and are increasingly considered to be the technology of choice for grid storage. In line with this increased applicability, there is also an increase in the development of new commercial lithium-ion cell technologies that incorporate innovative functional components (electrode material compositions and electrolyte formulations) and designs, leading to a diverse range of performance characteristics. The uniqueness of each technology in-turn gives rise to unique evolutions of cell performance as the cell degrades because of usage. Non-destructively measuring and subsequently tracking the evolution of lithium-ion cell characteristics is valuable for both industrial engineers and academic researchers. To proceed in this regard, stakeholders have often devised their own procedures for characterising lithium-ion cells, typically without considering unification, comparability or compatibility. This makes the comparison of technologies complicated. This comprehensive review for the first time has analysed and discusses the various international standards and regulations for the characterisation and electrical testing of lithium-ion cells, specifically for high-power automotive and grid applications

Design and use of multisine signals for Li-ion battery equivalent circuit modelling. Part 2 : model estimation

An Equivalent Circuit Model (ECM) of a lithium ion (Li-ion) battery is an empirical, linear dynamic model and the bandwidth of the input current signal and level of non-linearity in the voltage response are important for the model’s validity. An ECM is, however, generally parametrised with a pulse current signal, which is low in signal bandwidth (Part 1) and any non-linear dependence of the voltage on the current due to transport limitations is ignored. This paper presents a general modelling methodology which utilises the higher bandwidth and number of signal levels of a pulse-multisine signal to estimate the battery dynamics and non-linear characteristics without the need of a 3D look-up table for the model parameters. In the proposed methodology a non-parametric estimate of the battery dynamics and non-linear characteristics are first obtained which assists in the model order selection, and to assess the level of non-linearity. The new model structure, termed as the Non-linear ECM (NL-ECM), gives a lower Root Mean Square (RMS) and peak error when compared to an ECM estimated using a pulse data set