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Some Problems on the Analysis and Control of Electrical Networks with Constant Power Loads

Abstract : The continuously increasing demand of electrical energy has led to the conception of power systems of great complexity that may extend even through entire countries. In the vast majority of large-scale power systems the main primary source of energy are fossil fuels. Nonetheless, environmental concerns are pushing a major change in electric energy production practices, with a marked shift from fossil fuels to renewables and from centralized architectures to more distributed ones. One of the main challenges that distributed power systems face are the stability problems arising from the presence of the so-called Constant Power Loads (CPLs). These loads, which are commonly found in information and communication technology facilities, are known to reduce the effective damping of the circuits that energize them, which can cause voltage oscillations or even voltage collapse. In this thesis, the main contributions are focused in understanding and solving diverse problems found in the analysis and control of electrical power systems containing CPLs. The contributions are listed as follows. (i) Simply verifiable conditions are proposed to certify the non existence of steady states in general, multi-port, alternating current (AC) networks with a distributed array of CPLs. These conditions, which are based on Linear Matrix Inequalities, allow to discard the values of the loads' powers that would certainly produce a voltage collapse in the whole network. (ii) For general models of some modern power systems, including High-Voltage Direct Current transmission networks and microgrids, it is shown that if equilibria exist, then there is a characteristic high-voltage equilibrium that dominates, entry-wise, all the other ones. Furthermore, for the case of AC power systems under the standard decoupling assumption, this characteristic equilibrium is shown to be long-term stable. (iii) A class of port-Hamiltonian systems, in which the control variables act directly on the power balance equation, is explored. These systems are shown to be shifted passive when their trajectories are constrained to easily definable sets. The latter properties are exploited to analyze the stability of their---intrinsically non zero---equilibria. It is also shown that the stability of multi-port DC electrical networks and synchronous generators, both with CPLs, can be naturally studied with the proposed framework. (iv) The problem of regulating the output voltage of the versatile DC buck-boost converter feeding an {em unknown} CPL is addressed. One of the main obstacles for conventional linear control design stems from the fact that the system's model is non-minimum phase with respect to each of its state variables. As a possible solution to this problem, this thesis reports a nonlinear, adaptive controller that is able to render a desired equilibrium asymptotically stable; furthermore an estimate of the region of attraction can be computed. (v) The last contribution concerns the active damping of a DC small-scale power system with a CPL. Instead of connecting impractical, energetically inefficient passive elements to the existing network, the addition of a controlled DC-DC power converter is explored. The main contribution reported here is the design of a nonlinear, observer-based control law for the converter. The novelty of the proposal lies in the non necessity of measuring the network's electrical current nor the value of the CPL, highlighting its practical applicability. The effectiveness of the control scheme is further validated through experiments on a real DC network.
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Juan Eduardo Machado Martínez. Some Problems on the Analysis and Control of Electrical Networks with Constant Power Loads. Automatic. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLS445⟩. ⟨tel-02613958⟩

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