Wind energy is on an upswing due to climate concerns and increasing energy demands on conventional sources. Wind energy is attractive and has the potential to dramatically reduce the dependency on non-renewable energy resources. With the increase in wind farms there is a need to improve the efficiency in power allocation and power generation among wind turbines. Wake interferences among wind turbines can lower the overall efficiency considerably, while offshore conditions pose increased loading on wind turbines. In wind farms, wind turbines* wake affects each other depending on their positions and operation modes. Therefore it becomes essential to optimize the wind farm power production as a whole than to just focus on individual wind turbines. The work presented here develops a hierarchical power optimization algorithm for wind farms. The algorithm includes a cooperative level (or higher level) and an individual level (or lower level) for power coordination and planning in a wind farm. The higher level scheme formulates and solves a quadratic constrained programming problem to allocate power to wind turbines in the farm while considering the aerodynamic effect of the wake interaction among the turbines and the power generation capabilities of the wind turbines. In the lower level, optimization algorithm is based on a leader-follower structure driven by the local pursuit strategy. The local pursuit strategy connects the cooperative level power allocation and the individual level power generation in a leader-follower arrangement. The leader, could be a virtual entity and dictates the overall objective, while the followers are real wind turbines considering realistic constraints, such as tower deflection limits. A nonlinear wind turbine dynamics model is adopted for the low level study with loading and other constraints considered in the optimization. The stability of the algorithm in the low level is analyzed for the wind turbine angular velocity. Simulations are used to show the advantages of the method such as the ability to handle non-square input matrix, non-homogenous dynamics, and scalability in computational cost with rise in the number of wind turbines in the wind farm.

A fast and efficient method to calculate time schedules for internal and boundary PRVs and flow modulation curves has been developed and implemented. Both time and flow modulation can be applied to a single inlet DMA. The time modulation methodology is based on solving a nonlinear programming problem (NLP). In addition, Genetic Algorithms (GA) has been proposed and investigated to calculate the optimal coefficients of a second order relationship between the flow and the outlet pressure for a PRV to minimize the background leakage. The obtained curve can be subsequently implemented using a flow modulation controller in a feedback control scheme. The Aquai-Mod® is a hydraulic device to control and modulate the outlet pressure of a PRV according to the valve flow. The controller was experimentally tested to assess its performance and functionality in different conditions and operating ranges. The mathematical model of the controller has been developed and solved, in both steady state and dynamic conditions. The results of the model have been compared with the experimental data and showed a good agreement in the magnitude and trends. A new method for combined energy and pressure management via integration and coordination of pump scheduling with pressure control aspects has been created. The method is based on formulating and solving an optimisation NLP problem and involves pressure dependent leakage. The cost function of the optimisation problem represents the total cost of water treatment and pumping energy. Developed network scheduling algorithm consists of two stages. The first stage involves solving a continuous problem, where operation of each pump is described by continuous variable. Subsequently, the second stage continuous pump schedules are discretised using heuristic algorithm. Another area of research has been developing optimal feedback rules using GA to control the operation of pump stations. Each pump station has a rule described by two water levels in a downstream reservoir and a value of pump speed for each tariff period. The lower and upper water switching levels of the downstream reservoir correspond to the pump being “ON” or “OFF”. The achieved similar energy cost per 1 Ml of pumped water. In the considered case study, the optimal feedback rules had advantage of small number of ON/OFF switches, which increase the pump stations lifetime and reduce the maintenance cost as well.

Les premiers résultats en analyse convexe ne nécessitant aucune condition de qualification datent à peu près d'une quinzaine d'années et constituent le début de l'analyse convexe séquentielle. Ils concernaient essentiellement: la somme d'un nombre fini de fonctions convexes, la composition avec une application vectorielle convexe, et les problèmes de programmation mathématique convexe. Cette thèse apporte un ensemble de contributions à l'analyse convexe séquentielle. La première partie de la thèse est consacrée à l'obtention sans condition de qualification de règles de calcul sous-differentiel exprimées séquentiellement. On considère les cas suivants:l'enveloppe supérieure d'une famille quelconque de fonctions convexes semi-continues inférieurement définies sur un espace de Banach; une fonctionnelle intégrale convexe générale définie sur un espace de fonctions intégrales;la somme continue (ou intégrale) de fonctions convexes semi-continues inférieurement définies sur un espace de Banach séparable. Dans la deuxième partie on établit sans hypothèse de qualification sur les données du problème, des conditions nécessaires et suffisantes d'optimalité séquentielle pour divers types de problèmes d'optimisation et de contrôle optimal discret ou continu. / The first results in convex analysis without any qualificationcondition have been established fifteen years ago, and one may say thatsequential convex analysis began with those results. They essentially concerned:The finite sum of convex functions, the composition with a vectorvaluedconvex mapping, and convex mathematical programming. The firstpart of this dissertation provides several contibutions to sequential convexanalysis. The following cases are considered: the upper envelop of a familyof lower semicontinuous convex functions; the integral functional overan integral space; the continuous sum of lower semicontinuous convex functions.In the second part, necessary and sufficient optimality conditions areestablished in sequential form for many types of programming problems anddicrete or continuous optimal control problems.

The optimal steady-state control, and suboptimal adaptive control, of disturbed single-input-output systems are introduced, and the class of systems considered is defined. It is noted that the stochastic tracking problem divides into a deterministic tracking problem and a stochastic regulator problem; the solutions to these two problems are shown to be independent but formally similar. The continuous regulator problem is approached via both frequency and time domain methods: the former method is extended to cover unstable systems; the latter method is extended to include systems with input delay. The two regulators are shown to be externally equivalent. The frequency domain method is briefly described for discrete systems, and shown to include the minimum variance regulator of Åström and Peterka as a special case. Some systems which allow measurement noise to be treated as a system disturbance for the purposes of optimal controller design are investigated. A novel class of control laws is described in both continuous and discrete time; in the same way as the minimum variance regulator forms the basis of the self-tuning regulator of Åström and Wittenmark, these minimum variance controllers from the basis of a self-tuning controller. These minimum variance controllers have a number of advantages over the minimum-variance regulator, and are open to a number of interpretations including: a model following control law, and an extension of classical control laws to systems with delay. The optimality of this class of control laws is investigated, and analogies drawn with the previously considered k-step-ahead control laws; some examples are given to illustrate the method. An adaptive control law combining the above minimum variance controllers with a linear least-squares algorithm is proposed and shown to be self-tuning. These self-tuning controllers are only slightly more complex than the self-tuning regulator of Åström and Wittenmark, but have a number of advantages. Intuitive justification is given for the conjecture that some methods of Ljung, developed for the analysis of the self-tuning regulator, are applicable to the self-tuning controller. Simulated examples are given which compare and contrast the performance of the self-tuning controller with that of the self-tuning regulator. The first steps towards a quasi-continuous self-tuning controller are outlined.

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.

The concepts of engine downsizing and down-speeding offer reductions in CO2 emissions from passenger cars. These reductions are achieved by reducing pumping and friction losses at part-load operation. Conventionally, rated torque and power for downsized units are recovered by means of turbocharging. The transient response of such engines is, however, affected by the static and dynamic characteristics of the turbo-machinery. Recent advances in engine simulation and control tools have been employed for the purpose of the research reported in this thesis to identify and verify possible air-path enhancements. A systematic method for evaluating various turbocharger assistance concepts is proposed and discussed in this thesis. To ensure a fair comparison of selected candidate systems, an easily reconfigurable controller providing a close-to-optimal operation, while satisfying physical limits, is formulated. This controller is based on the Model Predictive Control framework and uses a linearised mean value model to optimise the predicted behaviour of the engine. Initially, the controller was applied to a 1D simulation model of a conventional light-duty Diesel engine, for which the desired closed-loop features were verified. This procedure was subsequently applied to various air-path enhancement systems. In this thesis, a turbocharger electric assistance and various concepts based on compressed gas injection were considered. The capability of these systems to improve engine response during third gear tip-in manoeuvre was quantified. This investigation was also complemented with a parametric study of how effectively each of the considered methods used its available resources. As a result, injecting compressed gas into the exhaust manifold was identified as an effective method, which to date has attracted limited attention from engine research community. The effectiveness of the exhaust manifold assistance was experimentally verified on a light-duty Diesel engine. The sensitivity of the improvements to compressed gas supply parameters was also investigated. This led to the development of the BREES system: a low component count, compressed gas based system for reducing turbo-lag. It was shown that during braking manoeuvres a tank can be charged to the level sufficient for a subsequent boost assistance event. Such a functionality was implemented with a very limited set of additional components and only minor changes to the standard engine control.

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The nonlinear simulation model of an unmanned aerial vehicle (UAV) in MATLAB&reg / /Simulink&reg / environment is developed by taking into consideration all the possible major system components such as actuators, gravity, engine, atmosphere, wind-turbulence models, as well as the aerodynamics components in the 6 DOF equations of motion. Trim and linearization of the developed nonlinear model are accomplished and various related analyses are carried out. The model is validated by comparing with a similar UAV data in terms of open loop dynamic stability characteristics. Using two main approaches / namely, classical and optimal, linear controllers are designed. For the classical approach, Simulink Response Optimization (SRO) tool of MATLAB&reg / /Simulink&reg / is utilized, whereas for the optimal controller approach, linear quadratic (LQ) controller design method is implemented, again by the help of the tools put forth by MATLAB&reg / . The controllers are designed for control of roll, heading, coordinated turn, flight path, pitch, altitude, and airspeed, i.e., for the achievement of all low-level control functions. These linear controllers are integrated into the nonlinear model, by carrying out gain scheduling with respect to airspeed and altitude, controller input linearization regarding the perturbed states and control inputs, and anti integral wind-up scheme regarding the possible wind-up of the integrators in the controller structures. The responses of the nonlinear model controlled with the two controllers are compared based on the military flight control requirements. The advantages and disadvantages of these two frequently used controllers in industry are investigated and discussed. These results are to be evaluated by the designers themselves based on the design criteria of a project that is worked on.

To reduce fossil fuel consumption and carbon emission in the building sector, renewable and low carbon energy technologies are integrated in building energy systems to supply all or part of the building energy demand. In this research, an optimal supervisory controller is designed to optimize the operational cost and the CO2 emission of the integrated energy systems. For this purpose, the building energy system is defined and its boundary, components (subsystems), inputs and outputs are identified. Then a mathematical model of the components is obtained. For mathematical modelling of the energy system, a unified modelling method is used. With this method, many different building energy systems can be modelled uniformly. Two approaches are used; multi-period optimization and hybrid model predictive control. In both approaches the optimization problem is deterministic, so that at each time step the energy consumption of the building, and the available renewable energy are perfectly predicted for the prediction horizon. The controller is simulated in three different applications. In the first application the controller is used for a system consisting of a micro-combined heat and power system with an auxiliary boiler and a hot water storage tank. In this application the controller reduces the operational cost and CO2 emission by 7.31 percent and 5.19 percent respectively, with respect to the heat led operation. In the second application the controller is used to control a farm electrification system consisting of PV panels, a diesel generator and a battery bank. In this application the operational cost with respect to the common load following strategy is reduced by 3.8 percent. In the third application the controller is used to control a hybrid off-grid power system consisting of PV panels, a battery bank, an electrolyzer, a hydrogen storage tank and a fuel cell. In this application the controller maximizes the total stored energies in the battery bank and the hydrogen storage tank.

Local electricity markets can be defined broadly as 'future electricity market designs involving domestic customers, demand-side response and energy storage'. Like current deregulated electricity markets, these localised derivations present specific stochastic optimisation problems in which the dynamic and random nature of the market is intertwined with the physical needs of its participants. Moreover, the types of contracts and constraints in this setting are such that 'games' naturally emerge between the agents. Advanced modelling techniques beyond classical mathematical finance are therefore key to their analysis. This thesis aims to study contracts in these local electricity markets using the mathematical theories of stochastic optimal control and games. Chapter 1 motivates the research, provides an overview of the electricity market in Great Britain, and summarises the content of this thesis. It introduces three problems which are studied later in the thesis: a simple control problem involving demand-side management for domestic customers, and two examples of games within local electricity markets, one of them involving energy storage. Chapter 2 then reviews the literature most relevant to the topics discussed in this work. Chapter 3 investigates how electric space heating loads can be made responsive to time varying prices in an electricity spot market. The problem is formulated mathematically within the framework of deterministic optimal control, and is analysed using methods such as Pontryagin's Maximum Principle and Dynamic Programming. Numerical simulations are provided to illustrate how the control strategies perform on real market data. The problem of Chapter 3 is reformulated in Chapter 4 as one of optimal switching in discrete-time. A martingale approach is used to establish the existence of an optimal strategy in a very general setup, and also provides an algorithm for computing the value function and the optimal strategy. The theory is exemplified by a numerical example for the motivating problem. Chapter 5 then continues the study of finite horizon optimal switching problems, but in continuous time. It also uses martingale methods to prove the existence of an optimal strategy in a fairly general model. Chapter 6 introduces a mathematical model for a game contingent claim between an electricity supplier and generator described in the introduction. A theory for using optimal switching to solve such games is developed and subsequently evidenced by a numerical example. An optimal switching formulation of the aforementioned game contingent claim is provided for an abstract Markovian model of the electricity market. The final chapter studies a balancing services contract between an electricity transmission system operator (SO) and the owner of an electric energy storage device (battery operator or BO). The objectives of the SO and BO are combined in a non-zero sum stochastic differential game where one player (BO) uses a classic control with continuous effects, whereas the other player (SO) uses an impulse control (discontinuous effects). A verification theorem proving the existence of Nash equilibria in this game is obtained by recursion on the solutions to Hamilton-Jacobi-Bellman variational PDEs associated with non-zero sum controller-stopper games.