186 research outputs found
Global Optimisation for Energy System
The goal of global optimisation is to find globally optimal solutions, avoiding local optima and other stationary points. The aim of this thesis is to provide more efficient global optimisation tools for energy systems planning and operation. Due to the ongoing increasing of complexity and decentralisation of power systems, the use of advanced mathematical techniques that produce reliable solutions becomes necessary. The task of developing such methods is complicated by the fact that most energy-related problems are nonconvex due to the nonlinear Alternating Current Power Flow equations and the existence of discrete elements. In some cases, the computational challenges arising from the presence of non-convexities can be tackled by relaxing the definition of convexity and identifying classes of problems that can be solved to global optimality by polynomial time algorithms. One such property is known as invexity and is defined by every stationary point of a problem being a global optimum. This thesis investigates how the relation between the objective function and the structure of the feasible set is connected to invexity and presents necessary conditions for invexity in the general case and necessary and sufficient conditions for problems with two degrees of freedom. However, nonconvex problems often do not possess any provable convenient properties, and specialised methods are necessary for providing global optimality guarantees. A widely used technique is solving convex relaxations in order to find a bound on the optimal solution. Semidefinite Programming relaxations can provide good quality bounds, but they suffer from a lack of scalability. We tackle this issue by proposing an algorithm that combines decomposition and linearisation approaches. In addition to continuous non-convexities, many problems in Energy Systems model discrete decisions and are expressed as mixed-integer nonlinear programs (MINLPs). The formulation of a MINLP is of significant importance since it affects the quality of dual bounds. In this thesis we investigate algebraic characterisations of on/off constraints and develop a strengthened version of the Quadratic Convex relaxation of the Optimal Transmission Switching problem. All presented methods were implemented in mathematical modelling and optimisation frameworks PowerTools and Gravity
A stability-theory perspective to synchronisation of heterogeneous networks
Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau
Linear Operation of Switch-Mode Outphasing Power Amplifiers
Radio transceivers are playing an increasingly important role in modern society. The
”connected” lifestyle has been enabled by modern wireless communications. The demand
that has been placed on current wireless and cellular infrastructure requires increased spectral
efficiency however this has come at the cost of power efficiency. This work investigates
methods of improving wireless transceiver efficiency by enabling more efficient power
amplifier architectures, specifically examining the role of switch-mode power amplifiers in
macro cell scenarios. Our research focuses on the mechanisms within outphasing power
amplifiers which prevent linear amplification. From the analysis it was clear that high power
non-linear effects are correctable with currently available techniques however non-linear effects
around the zero crossing point are not. As a result signal processing techniques for suppressing
and avoiding non-linear operation in low power regions are explored. A novel method of digital
pre-distortion is presented, and conventional techniques for linearisation are adapted for the
particular needs of the outphasing power amplifier. More unconventional signal processing
techniques are presented to aid linearisation of the outphasing power amplifier, both zero
crossing and bandwidth expansion reduction methods are designed to avoid operation in nonlinear
regions of the amplifiers. In combination with digital pre-distortion the techniques
will improve linearisation efforts on outphasing systems with dynamic range and bandwidth
constraints respectively.
Our collaboration with NXP provided access to a digital outphasing power amplifier,
enabling empirical analysis of non-linear behaviour and comparative analysis of behavioural
modelling and linearisation efforts. The collaboration resulted in a bench mark for linear
wideband operation of a digital outphasing power amplifier. The complimentary linearisation
techniques, bandwidth expansion reduction and zero crossing reduction have been evaluated in
both simulated and practical outphasing test benches. Initial results are promising and indicate
that the benefits they provide are not limited to the outphasing amplifier architecture alone.
Overall this thesis presents innovative analysis of the distortion mechanisms of the
outphasing power amplifier, highlighting the sensitivity of the system to environmental effects.
Practical and novel linearisation techniques are presented, with a focus on enabling wide band
operation for modern communications standards
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