High-power extracavity pulse compression in solid materials

A novel technique for high-power extracavity pulse compression with a nonlinear solid material is demonstrated. Before spectral broadening by self-phase modulation in the solid material, a short filament generated in argon is used as a spatial filter, which works for a uniform spectrum broadening over the spatial profile. Compensated by chirped mirrors, a 15-fs pulse is generated from a 32-fs input laser pulse. A total transmission larger than 80% after the solid material is achieved.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Reflection and transmission of Gaussian beam from a uniaxial crystal slab

We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Strategies for Power Line Communications Smart Metering Network Deployment

Smart Grids are becoming a reality all over the world. Nowadays, the research efforts for the introduction and deployment of these grids are mainly focused on the development of the field of Smart Metering. This emerging application requires the use of technologies to access the significant number of points of supply (PoS) existing in the grid, covering the Low Voltage (LV) segment with the lowest possible costs. Power Line Communications (PLC) have been extensively used in electricity grids for a variety of purposes and, of late, have been the focus of renewed interest. PLC are really well suited for quick and inexpensive pervasive deployments. However, no LV grid is the same in any electricity company (utility), and the particularities of each grid evolution, architecture, circumstances and materials, makes it a challenge to deploy Smart Metering networks with PLC technologies, with the Smart Grid as an ultimate goal. This paper covers the evolution of Smart Metering networks, together with the evolution of PLC technologies until both worlds have converged to project PLC-enabled Smart Metering networks towards Smart Grid. This paper develops guidelines over a set of strategic aspects of PLC Smart Metering network deployment based on the knowledge gathered on real field; and introduces the future challenges of these networks in their evolution towards the Smart Grid.

Linking energy policy, electricity generation and transmission using strong sustainability and co-optimization

The design of a sustainable electricity generation and transmission system is based on the established science of anthropogenic climate change and the realization that depending on imported fossil-fuels is becoming a measure of energy insecurity of supply. A model is proposed which integrates generation fuel mix composition, assignment of plants and optimized power flow, using Portugal as a case study. The result of this co-optimized approach is an overall set of generator types/fuels which increases the diversity of Portuguese electricity supply, lowers its dependency on imported fuels by 14.62% and moves the country towards meeting its regional and international obligations of 31% energy from renewables by 2020 and a 27% reduction in greenhouse gas emissions by 2012, respectively. The quantity and composition of power generation at each bus is specified, with particular focus on quantifying the amount of distributed generation. Based on other works, the resultant, overall distributed capacity penetration of 19.02% of total installed generation is expected to yield positive network benefits. Thus, the model demonstrates that national energy policy and technical deployment can be linked through sustainability and, moreover, that the respective goals may be mutually achieved via holistic, integrated design. ©2009 IEEE.

High-current adaptive impedance matching in narrowband power-line communication systems

This paper proposes a high current impedance matching method for narrowband power-line communication (NPLC) systems. The impedance of the power-line channel is time and location variant; therefore, coupling circuitry and the channel are not usually matched. This not only results in poor signal integrity at the receiving end, but also leads to a higher transmission power requirement to secure the communication process. To offset this negative effect, a high-current adaptive impedance circuit to enable impedance matching in power-line networks is reported. The approach taken is to match the channel impedance of N-PLC systems is based on the General Impedance Converter (GIC). In order to achieve high current a special coupler in which the inductive impedance can be altered by adjusting a microcontroller controlled digital resistor is demonstrated. It is shown that the coupler works well with heavy load current in power line networks. It works in both low and high transmitting current modes, a current as high as 760 mA has been obtained. Besides, compared with other adaptive impedance couplers, the advantages include higher matching resolution and a simple control interface. Experimental results are presented to demonstrate the operation of the coupler. © 2011 IEEE.

Experimental demonstration of a record high 11.25Gb/s real-time optical OFDM transceiver supporting 25km SMF end-to-end transmission in simple IMDD systems.

The fastest ever 11.25Gb/s real-time FPGA-based optical orthogonal frequency division multiplexing (OOFDM) transceivers utilizing 64-QAM encoding/decoding and significantly improved variable power loading are experimentally demonstrated, for the first time, incorporating advanced functionalities of on-line performance monitoring, live system parameter optimization and channel estimation. Real-time end-to-end transmission of an 11.25Gb/s 64-QAM-encoded OOFDM signal with a high electrical spectral efficiency of 5.625bit/s/Hz over 25km of standard and MetroCor single-mode fibres is successfully achieved with respective power penalties of 0.3dB and -0.2dB at a BER of 1.0 x 10(-3) in a directly modulated DFB laser-based intensity modulation and direct detection system without in-line optical amplification and chromatic dispersion compensation. The impacts of variable power loading as well as electrical and optical components on the transmission performance of the demonstrated transceivers are experimentally explored in detail. In addition, numerical simulations also show that variable power loading is an extremely effective means of escalating system performance to its maximum potential.

Adaptively modulated optical OFDM modems utilizing RSOAs as intensity modulators in IMDD SMF transmission systems.

Detailed investigations of the transmission performance of adaptively modulated optical orthogonal frequency division multiplexed (AMOOFDM) signals converted using reflective semiconductor optical amplifiers (RSOAs) are undertaken over intensity-modulation and direct-detection (IMDD) single-mode fiber (SMF) transmission systems for WDM-PONs. The theoretical RSOA model adopted for modulating the AMOOFDM signals is experimentally verified rigorously in the aforementioned transmission systems incorporating recently developed real-time end-to-end OOFDM transceivers. Extensive performance comparisons are also made between RSOA and SOA intensity modulators. Optimum RSOA operating conditions are identified, which are independent of RSOA rear-facet reflectivity and very similar to those corresponding to SOAs. Under the identified optimum operating conditions, the RSOA and SOA intensity modulators support the identical AMOOFDM transmission performance of 30Gb/s over 60km SMFs. Under low-cost optical component-enabled practical operating conditions, RSOA intensity modulators with rear-facet reflectivity values of >0.3 outperform considerably SOA intensity modulators in transmission performance, which decreases significantly with reducing RSOA rear-facet reflectivity and optical input power. In addition, results also show that use can be made of the RSOA/SOA intensity modulation-induced negative frequency chirp to improve the AMOOFDM transmission performance in IMDD SMF systems.

Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25 Gb/s optical OFDM signal transmission over 25 km PON systems.

The feasibility of utilising low-cost, un-cooled vertical cavity surface-emitting lasers (VCSELs) as intensity modulators in real-time optical OFDM (OOFDM) transceivers is experimentally explored, for the first time, in terms of achievable signal bit rates, physical mechanisms limiting the transceiver performance and performance robustness. End-to-end real-time transmission of 11.25 Gb/s 64-QAM-encoded OOFDM signals over simple intensity modulation and direct detection, 25 km SSMF PON systems is experimentally demonstrated with a power penalty of 0.5 dB. The low extinction ratio of the VCSEL intensity-modulated OOFDM signal is identified to be the dominant factor determining the maximum obtainable transmission performance. Experimental investigations indicate that, in addition to the enhanced transceiver performance, adaptive power loading can also significantly improve the system performance robustness to variations in VCSEL operating conditions. As a direct result, the aforementioned capacity versus reach performance is still retained over a wide VCSEL bias (driving) current (voltage) range of 4.5 mA to 9 mA (275 mVpp to 320 mVpp). This work is of great value as it demonstrates the possibility of future mass production of cost-effective OOFDM transceivers for PON applications.

Experimental demonstration of colourless real-time end-to-end optical OFDM transmission at 7.5Gb/s over 25km SSMF using a 1GHz RSOA

7.5Gb/s real-time end-to-end optical OFDM (OOFDM) transceivers incorporating variable power loading on each individual subcarrier are demonstrated experimentally, for the first time, using a live-optimized RSOA intensity modulator having a modulation bandwidth as narrow as 1GHz. Colourless real-time 16-QAM-encoded OOFDM signal transmission at 7.5Gb/s over 25km SSMF is achieved across the C-band in simple IMDD systems without in-line optical amplification and dispersion compensation. Copyright © 2010 The authors.

Experimental demonstration of real-time optical OFDM Transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA

The 7.5-Gb/s real-time end-to-end optical orthogonal frequency-division- multiplexing (OOFDM) transceivers incorporating variable power loading on each individual subcarrier are demonstrated experimentally using a live-optimized reflective semiconductor optical amplifier intensity modulator having a modulation bandwidth as narrow as 1 GHz. Real-time OOFDM signal transmission at 7.5 Gb/s over 25-km standard single-mode fiber is achieved across the $C$-band in simple intensity modulation and direct detection systems without in-line optical amplification and dispersion compensation. © 2006 IEEE.

Outage exponents of block-fading channels with power allocation

Power allocation is studied for fixed-rate transmission over block-fading channels with arbitrary continuous fading distributions and perfect transmitter and receiver channel state information. Both short- and long-term power constraints for arbitrary input distributions are considered. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. It is shown that the short- and long-term outage exponents for arbitrary input distributions are related through a simple formula. The formula is useful to predict when the delay-limited capacity is positive. Furthermore, this characterization is useful for the design of efficient coding schemes for this relevant channel model. © 2010 IEEE.