Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Grid-Forming Converter Control Method to Improve DC-Link Stability in Inverter-Based AC Grids

As renewable energy sources with power-electronic interfaces become functionally and economically viable alternatives to bulk synchronous generators, it becomes vital to understand the behavior of these inverter-interfaced sources in ac grids devoid of any synchronous generation, i.e. inverter-based grids. In these types of grids, the inverters need to operate in parallel in grid-forming mode to regulate and synchronize their output voltage while also delivering the power required by the loads. It is common practice, therefore, to mimic the parallel operation control of the very synchronous generators that these inverter-based sources are meant to replace. This practice, however, is based on impractical assumptions and completely disregards the key differences between synchronous machines and power electronic inverters, as well as the dynamics of the dc source connected to the inverter. This dissertation aims to highlight the shortcomings of conventional controllers and derive an improved grid-forming inverter controller that is effective in parallel ac operation without sacrificing dc-link stability. This dissertation begins with a basis for understanding the control concepts used by grid-forming inverters in ac grids and exploring where existing ideas and methods are lacking in terms of efficient and stable inverter control. The knowledge gained from the literature survey is used to derive the requirements for a grid-forming control method that is appropriate for inverter-based ac grids. This is followed by a review and comparative analysis of the performance of five commonly used control techniques for grid-forming inverters, which reveal that nested loop controllers can have a destabilizing effect under changing grid conditions. This observation is further explored through an impedance-based stability analysis of single-loop and nested-loop controllers in grid-forming inverters, followed by a review of impedance-based analysis methods that can be used to assess the control design for grid-forming inverters. An improved grid-forming inverter controller is proposed with a demonstrated ability to achieve both dc-link and ac output stability with proportional power-sharing. This dissertation ends with a summary of the efforts and contributions as well as ideas for future applications of the proposed controller

Eingangsadmittanz-Modellierung und passivitätsbasierte Stabilisierung von digital-stromgeregelten, netzgebundenen Umrichtern

Due to the ever increasing number of renewable energy systems in the electrical power grid, the application of power electronic-based circuits is gaining more and more importance. It has however been known for a while that interactions of one or multiple converters with resonances in the grid can lead to poorly damped oscillations, and thus, may threaten the stability of parts of the power system. The passivity theory has proven to be particularly powerful in preventing such situations. Accordingly, the stability of the power grid can be guaranteed by design if all components act passive. This means that all active loads and energy feeding converters have an input admittance with a non-negative real part. This can theoretically be achieved using passive or active damping strategies, but most research neglects real-world effects, which arise from the sampling of high-frequency switching harmonics. The aim of this dissertation is therefore to review the complete modeling and analysis of digitally current-controlled grid-connected converters and to extend the controller as well as filter design. On the basis of typical single-input single-output models of the converter’s input admittance, methods for the design of a passive damping or an active feed-forward are proposed and it is discussed which aspects have to be considered when implementing the filters. However, since the used models cannot reproduce all alias effects, in the further part of the thesis a multiple-input multiple-output converter model is developed. It is shown that the mirroring of high-frequency signal components onto low-frequency components can in principle be described by a dynamic uncertainty that affects the behavior of the converters' baseband dynamics. Due to this new insight it becomes clear which criteria passive or active filters should fulfill in order to specifically counteract the often negative mirroring effects of digital control. Finally, it is demonstrated that a robust passivation of the converter input admittance can prevent a destabilization of the power system by harmonics for a large number of grid impedances. The presented theory and the developed controller design are illustrated and verified by various simulations of an exemplary converter system.Aufgrund der immer größer werdenden Anzahl von erneuerbaren Energieanlagen im elektrischen Energieversorgungsnetz gewinnt der Einsatz von leistungselektronischen Schaltungen immer mehr an Bedeutung. Es ist jedoch seit längerem bekannt, dass Wechselwirkungen von einem oder mehreren Umrichtern mit Resonanzen im Netz zu schlecht gedämpften Schwingungen führen und damit die Stabilität von Teilen des Energienetzes gefährden können. Die Passivitätstheorie hat sich als besonders wirkungsvoll erwiesen, um solche Situationen zu verhindern. Demnach kann die Stabilität des Stromnetzes bereits in der Designphase gewährleistet werden, indem alle Komponenten passiv wirken. Das bedeutet, dass alle aktiven Verbraucher und einspeisenden Umrichter eine Eingangsadmittanz mit nicht negativem Realteil besitzen. Dies ist theoretisch mit Hilfe von passiven oder aktiven Dämpfungsstrategien zu erreichen. Die meisten Forschungsarbeiten vernachlässigen jedoch reale Effekte, die bei der Abtastung von hochfrequenten Harmonischen entstehen. Ziel dieser Dissertation ist es daher, den kompletten Modellierungs-, Analyse- und Regler- sowie Filterentwurfsprozess von digital-stromgeregelten, netzgebundenen Umrichtern zu überprüfen und zu erweitern. Auf der Basis typischer Eingrößenmodelle der Umrichter-Eingangsadmittanz werden Verfahren für die Auslegung einer passiven Dämpfung bzw. einer aktiven Vorsteuerung vorgeschlagen und es wird diskutiert, welche Aspekte bei der Implementierung der Filter zu berücksichtigen sind. Da sich mit den Modellen jedoch nicht alle Alias-Effekte abbilden lassen, wird im weiteren Teil der Arbeit ein Mehrgrößen-Umrichtermodell entwickelt. Es zeigt sich, dass die Spiegelung hochfrequenter Signalanteile auf niederfrequente Anteile prinzipiell durch eine dynamische Unsicherheit beschrieben werden kann, die das Grundfrequenzverhalten der Umrichter beeinflusst. Dank dieser neuen Erkenntnisse wird deutlich, welche Kriterien passive oder aktive Filter erfüllen sollten, um den oft negativen Spiegeleffekten der digitalen Regelung gezielt entgegenzuwirken. Es wird demonstriert, dass eine robuste Passivierung der Umrichter-Eingangsadmittanz eine Destabilisierung des Energienetzes durch Harmonische für eine Vielzahl von Netzimpedanzen verhindern kann. Die vorgestellte Theorie und der erarbeitete Reglerentwurf werden anhand diverser Simulationen eines beispielhaften Umrichtersystems verdeutlicht und validiert