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

Improvement of Stability of a Grid-Connected Inverter with an LCL filter by Robust Strong Active Damping and Model Predictive Control

This study addresses development and implementation of robust control methods for a three-phase grid-connected voltage source inverter (VSI) accompanied by an inductive-capacitive-inductive (LCL) filter. A challenge of current control for the VSI is LCL filter resonance near to the control stability boundary, which interacts with the inverter control switching actions and creates the possibility of instability. In general, active damping is needed to stabilize the system and ensure robust performance in steady-state and dynamic responses. While many active damping methods have been proposed to resolve this issue, capacitor-current-feedback active damping has been most widely used for its simple implementation. There has been no clear consensus regarding design of a control system including capacitor-current-feedback active damping. This is due to the fact that simulation/experiment results are not congruent with the design analyses on which the control is designed. This study explains the incoherence between theory and practice when it comes to a capacitor-currents-feedback active damping system. Proposed capacitor-current-estimate active damping utilizing a developed posteriori Kalman estimator gives coherent simulation results as expected from the design analyses. This reveals that the highly oscillatory capacitor currents containing the inverter switching effects bring about uncertainty in the system performance. The switching effects are not incorporated in the analyses and control system design. Therefore, it is required to remove the switching noise from the capacitor currents in order to yield consistent results. It has been confirmed that the proportional-negative feedback of the capacitor current is equivalent to virtual impedance connected in parallel with the filter capacitor. In a digitally controlled system, the computation delay causes the equivalent resistance of the virtual impedance to become negative in the frequency range of fs/6 to fs/2, which produces a pair of open-loop unstable poles in RHP. This happens when the displaced resonance peak by active damping is in that region. Thus, an a priori Kalman estimator has been developed to generate one-sample-ahead state variable estimates to reconstruct the capacitor currents for active damping, which can compensate for the delay. The one-sample-ahead capacitor-current estimates are computed from the inverter-side and grid-side current estimates. The proposed method provides extended limits of the active damping gain that improve robustness against system parameter variation. It also allows strong active damping which can sufficiently attenuate the resonance. Grid condition is another significant factor affecting the stability of the system. In particular, a weak grid tends to provide high impedance. The system employing the proposed active damping method stably operates in a weak grid, ensuring robustness under grid impedance variation. The developed Kalman estimators offer an effective and easy way of determining the stability status of a system in addition to the functions of filtering and estimation. Stability analysis can be easily made since state variable estimates go to infinity when a system is unstable. As a promising approach, model predictive control (MPC) has been designed for the system. This study suggests that MPC including active damping can be employed for a grid-connected VSI with an LCL filter with good dynamic performance