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Increasing penetration of non-synchronous generators (e.g. wind) would result in drastic reduction of the system (effective) inertia in future especially, during the low demand condition. Moreover, the possibility of larger and more frequent infeed losses is likely to cause unacceptably large variations in grid frequency and its rate-of-change (RoCoF). Restricting RoCoF within acceptable limits will be critical to avoid triggering of mains protection relays based on RoCoF which could lead to cascading outages and threaten system security. Rapid response from loads could be crucial in such situations to ensure secure operation of the system. Flexibility in certain types of loads could be exploited to provide fast and controllable power reserve if the supply voltage/frequency is controlled using the existing power electronic interfaces (e.g. motor drives) or additional ones like recently proposed 'Electric Spring' (ES). This thesis investigates the availability of fast shortterm power reserve from such controllable loads and shows their effectiveness in collectively contributing to inertial and/or primary frequency control. The proportion of different types of voltage-dependent loads varies depending on the time of the day. It is, therefore, important to determine the available reserve from such loads over the time horizon. The thesis proposes an online estimation method which can be used by the system operators to estimate available reserve in real time and schedule other forms of reserves accordingly. For practical implementation of ES in future distribution networks, it is important to investigate the operation of multiple such devices and their interaction with the change in network parameters. This thesis has developed both the time and frequency-domain models to study the control loop dynamics of ES in order to mitigate any adverse interaction.

The present work investigates a number of problems related to the modelling and approximation of nonlinear systems, using geometry as the primary lens through which ideas are explored. The first part of the work focuses on the fundamental problems of system identification and model reduction for nonlinear systems. Three different approaches to the identification of nonlinear systems are developed using nonlinear realization theory, ideas from subspace identification and functional equations. The model reduction problem at isolated singularities is then posed and solved using the concept of moment matching. Motivated by these results, the second part of the work develops several notions and tools for modelling nonlinear systems. First, a nonlinear enhancement of the notions of eigenvalue and of pole is introduced and studied exploiting the differential geometric approach to nonlinear systems. The persistence of excitation of signals generated by autonomous systems is then characterized in geometric terms. Finally, connections between moments of systems and moments of random variables are established. The theory is illustrated by means of several examples and the applicability of the resulting algorithms is verified by numerical simulations.

Human bodies are governed by multiple interacting functions – cardiac, neural, and respiratory to name a few. To assess the health of a high-risk person or as part of an ordinary medical check-up, a wearable device would allow users to continue with their daily routine. Therefore, the ultimate aim in mobile physiological monitoring is to design a single unobtrusive device that observes and analyses as many body parameters as accurately as possible. This would enhance the user’s quality of life, provide a more natural setting for health assessment, and equip physicians with continuous real-world data they could not study previously. Existing wearable solutions are either obtrusive or only cover a subset of the body functions (or both). In this work, the ear canal is investigated as a base for a mobile multi-function health monitor that is as unnoticable as hearing devices worn by millions of people every day. So far, head-based locations for recording physiological signals other than brain rhythms have been underexplored, as the comparatively narrow neck impedes the propagation of vital signals from the torso to the head surface. The suitability of the ear canal as a location for meaningful observations of physiological signals is first shown through a novel three-dimensional multi-shell biophysics model with realistic body geometries and dielectric properties, which is used to simulate the propagation of biosignals from their sources to the sensor positions on the head and in the ear. After establishing the theoretical principles behind cardiac and neural recordings from in-ear locations, the feasibility of such measurements is demonstrated through experiments. Starting with sensors embedded in a motorcycle helmet – also concealed in scenarios where a helmet is routinely worn – standard brain responses are reliably determined and heart beats correctly detected using a novel multi-channel algorithm in real-world scenarios during motion. Furthermore, full cardiac cycles are extracted from the noisy head-ECG, which facilitates an early warning system for the diagnosis of cardiovascular diseases. Subsequently, this methodology is proven to work with sensors embedded onto earplugs. The straightforward helmet and in-ear set-ups permit their usage in everyday life and enable the analysis of changes in vital body parameters. A new perspective on the evaluation of heart rate changes for stress analysis is next developed, by a simultaneous consideration of multiple heart rate derived stress metrics to categorise the psychological and physiological state of a person. The proposed theoretical models, conducted experiments, and developed algorithms pave the way to 24/7 continuous and inconspicuous health monitoring and promise to empower practitioners with a unique long-term data source for prescribing treatment.

In recent years, stochastic geometry has emerged as a powerful tool for the modeling, analysis, and design of wireless networks with random topologies. Stochastic geometry has been demonstrated to provide a tractable yet an accurate approach for the performance analysis of wireless networks, when the network nodes are modeled as a Poisson point process. This thesis develops analytical frameworks to study the performance of various large-scale wireless networks with random topologies. Firstly, it develops a mathematical model for the uplink analysis of heterogeneous cellular networks when the base stations have multiple antennas. Further, it studies how the gains of downlink and uplink decoupling can be optimized in such a network. Secondly, this thesis also models, analyzes, and designs an ad-hoc network architecture that utilizes both the wireless power transfer and backscatter communications. The performance of such a network is further compared with a regular powered network. Finally, this thesis for the first time develops a scheduling algorithm for cellular networks that has an information theoretic justification. Then using tools from stochastic geometry, this thesis quantifies the gains of such scheduling algorithm over the traditional scheduling algorithm for the downlink transmission. Furthermore, to find the optimal system parameters that provide the maximum gains, this thesis performs asymptotic analysis and provides a simple optimization algorithm. The accuracy of all the mathematical models have been verified with extensive Monte Carlo simulations.

Nano-scale fabrication of technical materials is one of the biggest challenges in future industrial applications. There is a growing need for components with feature sizes below one micron. The well-established techniques, including e-beam lithography and focused ion beam milling, suffer several limitations, such as expensive apparatus, low fabrication speed and small scale production. Laser nano-ablation, as an efficient implementation method, has offered promising merits in large scale nano-fabrication. First applied to polymers, it offered a one-step fabrication ability with sub-micron structuring resolution. Later, following the pioneering work of Stuke and co-workers, surface treatment of non-polymeric materials, such as crystals, metals and semiconductors was achieved using picosecond and femtosecond laser systems. In this thesis, laser nano-ablation was used to fabricate large scale nano-hole arrays on polyimide films to improve the performance of humidity sensors. A 193 nm ArF pulsed laser system was established, simulated and optically aligned. Hole arrays with 920 nm diameter at the top, 339 nm diameter at the bottom and 451 nm depth were produced using mask projection ablation on polyimide films. Interdigitated polyimide humidity sensors were fabricated, packaged and tested. Based on conformal mapping and partial capacitance, capacitance modelling of interdigitated electrode arrays was built to analyse the capacitance variations with electrode dimensions. A reliable home-made humidity chamber was established for sensor tests. Static and dynamic tests were carried out to characterize the sensor performance. Static tests showed the nano-patterned films can enhance the sensitivity by 7.1% at humidity levels below 68% RH and by 100% at humidity levels higher than 68% RH. In addition, dynamic test showed that the nano-patterned polyimide films are able to improve the response speed by about 20%. Overall, this thesis demonstrates that large-area nano-hole arrays formed by laser ablation can improve the sensitivity and response time of polyimide-based capacitive humidity sensors.

Anastomotic leakage (AL) is the leading cause of morbidity and mortality after bowel anastomosis, a surgical procedure used to restore luminal continuity after bowel tumour resection. Even after years of research, its occurrence has not decreased, and new methods of monitoring the wound and predicting anastomotic failure are therefore urgently required. Here we propose the use of an internal coil to increase the signal-to-noise ratio (SNR) during Magnetic Resonance Imaging (MRI ) and/or Spectroscopy (MRS). Both methods may be used to identify ischemia and oedema, considered to be clinical indications of AL. The annular nature of the anastomotic surgical wound suggests the use of a coil with an annular field-of view, mounted on a Biodegradable Anastomosis Ring (BAR), a surgical device commonly used as a temporary mechanical support that is fragmented and excreted from the body after wound healing. The proposed solution is a Magneto-Inductive (MI) ring resonator, based on a set of magnetically coupled L-C resonators. Its advantages are that its separate elements fit comfortably inside the BAR, are not mechanically connected, and consequently may be fragmented and excreted with the BAR itself. A coupled pair of 8-element MI ring resonators is proposed, operating on an anti-symmetric spatial mode to avoid coupling to the B1 field during the excitation phase of MRI. However, the electrical response of an early prototype shows that insufficient rejection of uniform fields is achieved using the most obvious arrangement. Therefore, a search of the effect of design parameters on the spectra of resonant modes supported by the electrical system is carried out to identify an arrangement offering improved decoupling. A suitable design is developed, based on physical overlap between adjacent elements in the same ring, which alters the sign and magnitude of a key magnetic coupling coefficient. MRI fields-of-view are theoretically estimated for several different arrangements for signal extraction, including devices that are mutually coupled to an external read coil and directly coupled devices. Difficulties with combining mutual coupling and B1 field rejection are identified, and wired connections are proposed as a solution. It is found that a device with a single such connection gives a sensitivity pattern with partial symmetry, whereas a quadrature tap restores full symmetry. In vitro 1H MRI is then carried out at 1.5 T and 3.0 T using agar gel immersion phantoms, both for mutually coupled systems and for directly coupled systems. As expected, mutual coupling is found to be an unsuitable readout method for a device operating on its anti-symmetric mode, but does allow analysis of the effectiveness of B1 field decoupling. Directly coupled devices operate essentially as expected, providing up to 15-fold local enhancement in SNR, compared to the system body coil.

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