Input-Admittance Passivity Compliance for Grid-Connected Converters With an LCL Filter

This work presents a design methodology and its experimental validation for the input-admittance passivity compliance of LCL grid-connected converters. The designs of the LCL filter parameters and discrete controller are addressed systematically, and suitable design guidelines are provided. The controller design is developed in the z-domain, with capacitor voltage based active damping used as degree of freedom to compensate for system delay effects. The role of resistive components in the circuit, which have inherent dissipative properties, is also discussed. As an outcome of the design, a passive input admittance shaping is obtained. The theoretical development is further verified in a low-scale prototype supplied from a controllable grid simulator. For the sake of generality, different combinations of resonant to sampling frequency are tested. Experimental results fully prove the input-admittance passivity compliance

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

Passivation of Grid-Following VSCs: A Comparison Between Active Damping and Multi-Sampled PWM

This article compares different strategies used to enhance the stability properties of grid-following voltage-source converters (VSCs). Because of digital delays, VSC admittance exhibits a nonpassive zone, which introduces negative damping and may destabilize the grid-connected operation. It is shown that typically used active damping (AD) strategies only bring positive impact up to a certain frequency, while deteriorating admittance properties around and above the Nyquist frequency. Multi-sampled pulsewidth modulation (MS-PWM) greatly extends the passive admittance region, using only a single-loop current controller. Experimental admittance measurements are performed on a single-phase VSC, up to twice the switching frequency. Subsequently, different grid-connected scenarios are tested to show that MS-PWM retains stable operation, where AD methods cause instability. This article also offers analytic modeling and experimental measurements of noise propagation for compared strategies. It is shown that derivative-based AD is not highly sensitive; however, MS-PWM offers additional noise suppression

A Passivity-Based High-Bandwidth Voltage Control for Grid-Forming Inverters

The increasing number of power electronic devices connected to the power system is leading it to new stability challenges. The uncertainty of the grid-model may complicate the controller design and compromise stability. As a countermeasure, LQR and pole-placement techniques can be re-oriented to design for passivity, which is leading to new controller design paradigms. Nevertheless, as a general rule, all the variables of the system are considered in the full bandwidth, which may become unfeasible or costly in the industrial scenario. An original controller design technique for LC or LCL filter which accomplishes passivity in a wide range of frequency is proposed. Besides, it reduces the voltage sensor needs, even controlling it, being suitable for Grid-Forming. As consequence, the complexity of the software, hardware and price are reduced. Experimental verification is provided: impedance of the converter from the grid side and response against a changes in the reference/load

A Root-Locus Design Methodology Derived from the Impedance/Admittance Stability Formulation and Its Application for LCL Grid-Connected Converters in Wind Turbines

This paper presents a systematic methodology for the design and the tuning of the current controller in LCL grid-connected converters for wind turbine applications. The design target is formulated as a minimization of the current loop dominant time constant, which is in accordance with standard design guidelines for wind turbine controllers (fast time response and high stability margins). The proposed approach is derived from the impedance/admittance stability formulation, which, on one hand, has been proved to be suitable for the controller design when the active damping is implemented and, on the other hand, has also been proved to be very suitable for system-level studies in applications with a high penetration of renewable energy resources. The tuning methodology is as follows: first, the physical system is modeled in terms of the converter admittance and its equivalent grid impedance; then, a sensitivity transfer function is derived, from which the closed-loop eigenvalues can be calculated; finally, the set of control gains that minimize the dominant time constant are obtained by direct search optimization. A case study that models the target system in a low-power scale is provided, and experimental verification validates the theoretical analysis. More specifically, it has been found that the solution that solves the minimization of the current controller time constant (wind turbine controller target) also corresponds to a highly damped electrical response (robustness provided by the active damping)

Optimal model reference control design for grid connected voltage source converters

Texto en inglés y resumen en inglés y españolEsta tesis se centra en el diseño de controladores H∞ basados en modelos de referencia para su aplicación en el control de convertidores electrónicos de potencia en fuente de tensión (VSC). Se persiguen dos objetivos: el conformado de la admitancia de entrada de un VSC controlado en corriente y el óptimo amortiguamiento activo de filtros resonantes.El diseño de controladores óptimos H∞ aporta ciertas ventajas con respecto al diseño clásico. La principal técnica de diseño H∞ utilizada en la literatura se centra en la minimización de la función de sensibilidad. Ésta permite lidiar con diferentes problemas de compromiso en el diseño de controladores de forma sencilla, como el conformado de la función de lazo, el seguimiento de referencias, la estabilidad del sistema o la limitación del ancho de banda de control. Sin embargo, esta técnica carece de la habilidad de conformar la fase de funciones en lazo cerrado. La técnica H∞ basada en modelos de referencia soluciona este problema.La principal contribución de esta tesis es la aplicación de esta técnica para el moldeado de la admitancia en lazo cerrado de VSCs, la cual juega un importante papel tanto en la estabilidad de sistemas complejos como en la mejora de la calidad de energía en la red. Utilizando la técnica propuesta, el diseñador podrá especificar, en un gran ancho de banda y en un solo marco de diseño, tanto la admitancia del convertidor del convertidor (en modulo y en fase), como el comportamiento del seguimiento de referencias. El proceso de diseño finaliza con la síntesis de un controlador discreto ejecutable en una plataforma digital (DSP).Las posibilidades que presenta esta nueva metodología de diseño son amplias. La presente propuesta se ilustra con el control de un rectificador activo conectado a la red, pero es lo suficientemente flexible como para aplicarse en otros esquemas de control y topologías de convertidor. Se considerarán tres aplicaciones del control de admitancia: el diseño de aplicaciones resistivas en un gran ancho de banda, las cuales mejoran la robustez en la conexión estable a red débiles, el diseño de aplicaciones con una admitancia baja, las cuales mejoran el rechazo de (sub/inter)armónicos de la tensión de red en el control de corriente, y el diseño de aplicaciones con una admitancia alta, que al conectarse en paralelo a la red actúan como estabilizadores de ésta. La metodología de diseño de cada controlador, así como sus limitaciones, implementación y los resultados experimentales obtenidos son detallados.De forma complementaria, se explora la técnica de diseño basada en modelos de referencia para el amortiguamiento óptimo de resonancias en filtros LCL. La idea es diseñar un amortiguador activo que, una vez conectado, moldee la dinámica del filtro LCL de tal manera que este se comporte como un filtro L. Esto permitirá el posterior uso de sencillos controladores de corriente diseñados para filtro L, evitando la complejidad del diseño de controladores para filtros LCL, sin renunciar con ello a su gran capacidad de filtrado. La metodología de diseño es lo suficientemente general como para presentar diferentes estructuras de entrada/salida para el amortiguador. Los resultados obtenidos demuestran la mejora en la robustez del sistema

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

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