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Distributionally robust control and optimization




Switched mode electric power converters are important components in today’s electricity dependent world. They interface power sources, grids, and consumers that operate at different AC and DC voltage levels. Their performance is a topic of growing interest, as high performance converters enable efficient, grid-friendly energy conversion and compact converter design. This dissertation aims at enhancing the performance of switched mode electric power converters through control. To achieve this, optimisation-based control approaches are sought that are applicable to a wide class of converters.

First, a modelling framework is established that forms the basis for these control approaches. The framework features a discrete time model of the system dynamics, that accurately captures the switched system behaviour without constraining the modulation to predefined switching patterns. It furthermore includes relevant system outputs such as the power transfer and important performance measures such as reference tracking and conversion losses. As all models are compatible with the mixed-logical-dynamical (MLD) framework [7], the modelling framework allows for formulating mixed integer optimisation problems to find the converter operation for optimal system performance that are suitable for commercially available optimisation software. Next, the framework is employed in two optimisation-based control methods: Model predictive control and optimisation-based control of cyclic systems.

In the second part of this thesis, the modelling framework is used in four different model predictive control (MPC) schemes. They differ in model accuracy, i.e. discretisation rate of the dynamics, and control update rate. The first presented scheme is averaging MPC, where the controller is updated once per switching period. This scheme is based on the commonly used averaged model of the system dynamics, which is obtained straightforwardly in the modelling framework by choosing the discretisation equal to the switching frequency. The resulting optimisation problems are generally linear or quadratic programs. The second scheme, intersampling MPC as presented e.g. in [ 5] or [31], uses more accurate, hybrid models with a higher discretisation frequency and the same control update rate as averaging. Using the presented modelling framework, this more accurate model of the system dynamics allows for including performance measures such as conversion losses in the MPC problem, resulting in linear or quadratic mixed integer programs. The third scheme, the herein proposed multisampling MPC, combines the model accuracy and corresponding benefits of intersampling MPC with a higher control update rate, which allows for faster reaction to disturbances. The formulation of averaging, intersampling, and multisampling MPC using the modelling framework is illustrated for a buck converter in simulation. Finally, the fourth MPC scheme, originally published in [54], is here presented as averaging MPC with multisampled filtering. The accurate model of the system dynamics with a high discretisation rate is employed to estimate the rippling states and their averages. This allows to make better use of available measurement, as every sample contributes to the state estimate, and prevents the ripple from entering the control feedback loop. The optimsation problem is formulated based on the average, ripple-free dynamics, resulting in optimisation problems of similar complexity to the averaging approach. The effectiveness of the scheme is demonstrated in simulation for a single phase grid inverter, that is operated at a low switching frequency and where the control goals are a high power factor and rejection of low-order harmonics.

In some applications, dynamic control using MPC approaches based on hybrid models yields optimisation problems that are computationally prohibitive. For such cases, the use of the framework to find optimal cyclic steady state operation is proposed. The optimisation problems are solved offline and the resulting optimal modulation patterns are stored in a look-up table. As an example application of the approach, the class of multisource converters is presented. The control goal is to minimise conversion losses. The effectiveness of the approach is first investigated in simulation for a twosource converter where the impact of the resistance on the dynamics is negligible. The proposed scheme is compared to two state-of-the-art approaches: the commonly used rectangular modulation and the close to optimal modulation for reduced switching losses in [ 65]. An extension of the proposed approach for the given application is presented. It allows for finding the loss-optimal switching frequency at each operating point. Its impact is assessed in simulation. Finally, the effectiveness and real-time applicability of the proposed look-up table based approach is demonstrated experimentally on a twosource lab setup. In this setup, the impact of the resistance on the system dynamics is not negligible. While the optimisation-based approaches found in literature do not consider this scenario, the proposed approach is directly applicable. To assess both, dynamic performance and efficiency of the controller, an experimental protocol is presented that only uses the measurements necessary for control, allows for in-lab testing of twosource power converters, and scales to high power applications.

In summary, this thesis presents an MLD-compatible modelling framework that captures important properties of a class of switched mode electric power converters, its use in different optimisation-based control approaches, and the resulting performance improvements in selected applications.

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Type of Publication:

(03)Ph.D. Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2015:IFA_5353,
    title={{Distributionally robust control and optimization}},
    school={ETH Zurich},
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