Design for Passivity in the Z-Domain for LCL Grid-Connected Converters

This paper develops a design methodology aimed to shape passive the admittance of the LCL grid-connected voltage source converters (VSCs). A novel aspect of this work is the assessment of the range of frequencies for control design: due to discrete and PWM operation, the effectiveness of the control action is more and more reduced as frequency increases; in practice, system delays and non-linear effects tend to impair the passivity properties and also its experimental validation. However, as shown in this paper, those effects can be minimised by including the LCL filter as a part of an outer VSC admittance: this assumption is supported by the fact that high frequency disturbances (generated in the point of connection) are absorbed by the LCL capacitor branch, and hence, are not able to create a positive feedback in the VSC (i.e., the active component). By taking advantage of this remark, the inner VSC admittance can be shaped by a reduced order filter in the Z-domain, which mainly depends on the proportional and active damping (controller) gains. The design hypotheses and the control design methodology are verified by PLECS switching-mode simulations

Stable and Passive High-Power Dual Active Bridge Converters Interfacing MVDC Grids

Dual active bridge (DAB) is a topology that is receiving more and more attention as a potential solution to interface dc grids of different voltage levels. From a system level, the implications of DABs on the stability of complex power systems are addressed in this work. Dynamics modelling and stability assessment for a DAB implementation aimed to interface low-voltage energy resources with a medium-voltage dc (MVDC) collection and distribution grid are presented. The DAB admittance is analytically derived and assessed in order to describe its dynamics and anticipate its behavior when integrated in a complex MVDC grid. The model considers the low frequency range, mostly dominated by the controller action, and the high frequency range, described by a non-linear operation. The theoretical analysis is verified by hardware-in-the-loop emulation, with the controller running on a digital signal processor. The proposed implementation is proved to achieve passivity in the whole spectrum, which undoubtedly is a desired feature for a massive power electronics integration in the future MVDC grids

Multi-Variable High-Frequency Input-Admittance of Grid-Connected Converters: Modeling, Validation and Implications on Stability

Modern grids are facing a massive integration of power electronics devices, usually associated to instability issues. In order to assess the likelihood and severity of harmonic instability in the high frequency region, this work develops a multi-variable input-admittance model that accurately reflects the following aspects: i) the discrete controller frequencies are defined inside a spectrum region limited by the Nyquist frequency; ii) the physical system aliases are transformed into lower frequency component inside the discrete controller. The proposed model shows that dynamic interactions are not theoretically band-limited; however, the control action tends to be strongly limited in a low frequency range, due to the natural low-pass filter behavior of acquisition and modulation blocks. This is reflected in a reduced resistive part (either positive or negative) of the input-admittance in the high frequency range. More specifically, considering the input-admittance passivity criterion, the excursions into the non-passive area are very smooth at high frequencies, where the input-admittance is well described by simply its inductive filter. Comprehensive experiments are conducted on a lab scale prototype, which includes measurements beyond the Nyquist frequency and alias identification. The experimental results well match the theoretical model

Factors in Active Damping Design to Mitigate Grid Interactions in Three-Phase Grid-Connected Photovoltaic Inverters

An LCL filter provides excellent mitigation capability of the switching frequency harmonics, and is, therefore, widely used in grid-connected inverter applications. The resonant behavior induced by the filter must be attenuated with passive or active damping methods in order to preserve the stability of the grid-connected converter. Active damping can be implemented with different control algorithms, and it is frequently used due to its relatively simple and low-cost implementation. However, active damping may easily impose stability problems if it is poorly designed.This thesis presents a comprehensive small-signal model of a three-phase grid-connected photovoltaic inverter with LCL filter. The analysis is focused on a capacitor-currentfeedback (i.e., a multi-current feedback) active damping and its effects on the system dynamics. Furthermore, a single-current-feedback active damping technique, which is based on reduced number of measurements, is also studied. The main objective of this thesis is to present an accurate multi-variable small-signal model for assessing the control performance as well as the grid interaction sensitivity of grid-connected converters in the frequency domain.The state-of-the-art literature studies regarding the active damping are mainly concentrated on stability evaluation of the output-current loop, and the effect on external characteristics such as susceptibility to background harmonics and impedance-based instability has been overlooked. As the active damping affects significantly the sensitivity to grid interactions, accurate predictions of the system transfer functions, e.g. the output impedance, must be utilized in order to assess the active-damping-induced properties. Moreover, the single-current-feedback active damping method lacks the aforementioned analysis in the literature and, therefore, the need for accurate full-order small-signal models is evident.This thesis presents design criteria for the active damping in a wide range of operating conditions. Accordingly, peculiarities regarding the active damping are discussed for both multi and single-current-feedback active damping schemes. In addition, the parametric influence of the active damping on the output-impedance characteristics is explicitly analyzed. It is shown that the active damping design has a significant effect on the output impedance and, therefore, the impedance characteristics should be considered in the converter design for improved robustness against background harmonics and impedancebased interactions

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