Non-linear model predictive energy management strategies for stand-alone DC microgrids

Due to substantial generation and demand fluctuations in stand-alone green micro-grids, energy management strategies (EMSs) are becoming essential for the power sharing purpose and regulating the microgrids voltage. The classical EMSs track the maximum power points (MPPs) of wind and PV branches independently and rely on batteries, as slack terminals, to absorb any possible excess energy. However, in order to protect batteries from being overcharged by realizing the constant current-constant voltage (IU) charging regime as well as to consider the wind turbine operational constraints, more flexible multivariable and non-linear strategies, equipped with a power curtailment feature, are necessary to control microgrids. This dissertation work comprises developing an EMS that dynamically optimises the operation of stand-alone dc microgrids, consisting of wind, photovoltaic (PV), and battery branches, and coordinately manage all energy flows in order to achieve four control objectives: i) regulating dc bus voltage level of microgrids; ii) proportional power sharing between generators as a local droop control realization; iii) charging batteries as close to IU regime as possible; and iv) tracking MPPs of wind and PV branches during their normal operations. Non-linear model predictive control (NMPC) strategies are inherently multivariable and handle constraints and delays. In this thesis, the above mentioned EMS is developed as a NMPC strategy to extract the optimal control signals, which are duty cycles of three DC-DC converters and pitch angle of a wind turbine. Due to bimodal operation and discontinuous differential states of batteries, microgrids belong to the class of hybrid dynamical systems of non-Filippov type. This dissertation work involves a mathematical approximation of stand-alone dc microgrids as complementarity systems (CSs) of Filippov type. The proposed model is used to develop NMPC strategies and to simulate microgrids using Modelica. As part of the modelling efforts, this dissertation work also proposes a novel algorithm to identify an accurate equivalent electrical circuit of PV modules using both standard test condition (STC) and nominal operating cell temperature (NOCT) information provided by manufacturers. Moreover, two separate stochastic models are presented for hourly wind speed and solar irradiance levels

Measurements, Models, Systems and Design

531 s.

H∞ Suboptimal Tracking Control for Bilinear Power Converter Systems with Dynamic Feedback - Theory and Experiment

In this thesis, bilinear power converters are considered that arise for state-averaged models in continuous conduction mode. Since such power converters are often not feedback linearizable with respect to the output to be controlled,they are an interesting and demanding class of control systems. One control objective for the considered system class is to include trajectory tracking in the system equations. With a state and input transformation into the so called error system representation, where the error between real variables and reference variables is considered, the error system equations show to be time-varying. Another objective is to cope with disturbances, noise, parameter uncertainties, etc. Therefore, integral feedback is included in the feedback strategy, which leads to input-affine systems with a special structure due to the originally bilinear system equations. A slightly different strategy is a disturbance feedback approach. It addresses the same control objectives, is structurally similar to integral feedback and allows for more freedom in choice of feedback design parameters. However, it is less general and requires online-replanning of the reference trajectory. For state feedback design, we choose H∞ control with a quadratic performance functional since we want to have low control effort and want to keep the error of the output to be controlled small in case of appearing disturbances. Finally, so as to address stability properties in the closed-loop, integral Input-to-State Stability (iISS) theory is a good choice to cope with nonzero disturbances. In order to guarantee stability for the closed-loop system in the presence of disturbances, we link the solution of the nonlinear H control problem with iISS. It is possible to derive conditions, when the suboptimal state feedback H∞ control problem for the bilinear power converter systems with integral feedback / disturbance feedback and trajectory tracking can be solved. At the same time, it can be shown that the closed-loop systems is iISS. To underline the generality of the approach, the obtained theory for bilinear power converter systems is extended to general bilinear systems and it is even possible to discuss the more demanding multiple-input case. Equipped with the required theory to solve the posed control problem, we address the experimental setup of a boost converter / DC motor system. Here, the control task is to track the angular velocity of the motor shaft and attenuate appearing load disturbances. Therefore, we implement disturbance feedback and proof boundedness of trajectories for the online-replanning of the approximate trajectory generation method. Various experiments are presented in order to investigate the applicability of the approach.In der vorliegenden Dissertation werden bilineare Leistungskonvertersysteme untersucht, wie sie für Modellgleichungen mit gemittelten Zuständen im kontinuierlichen Betrieb (engl. "continuous conduction mode")auftreten. Da eine große Zahl dieser Leistungskonverter nicht eingangs-zustandslinearisierbar hinsichtlich des Regelausgangs und dann oft sogar nicht-minimalphasig sind, zählen sie zur Klasse der schwierig zu regelnden Systeme. Ein Regelungsziel für die betrachtete Systemklasse ist die Berücksichtigung von Referenztrajektorien für einen Wunschausgang des Systemmodells. Dazu wird ein sogenanntes Fehlersystem eingeführt, das die Differenz zwischen tatsächlichen Größen und Referenzgrößen widerspiegelt. Aufgrund der Bilinearität der ursprünglichen Modellgleichung ist dieses Fehlersystem dann zeitvariant. Ein weiteres Ziel ist das Ausregeln von auftretenden Störungen, Messrauschen, Modellunsicherheiten, usw., was üblicherweise anhand eines Integratoranteils (kurz: I-Anteils) im Regelgesetz berücksichtigt wird. Ein I-Anteil ist eine dynamische Erweiterung der Zustandsgleichungen und führt zu einem zusätzlichen Zustand. Damit die zusätzliche Differentialgleichung nicht entkoppelt vorliegt, muss mit einer geeigneten Eingangstransformation dafür gesorgt werden, dass der Integriererzustand im Regelgesetz vorkommt. Dadurch wird jedoch die ursprüngliche Bilinearität der Gleichungen zerstört, so dass am Ende ein eingangsaffines System vorliegt, das aber natürlich aufgrund der Bilinearität der ursprünglichen Systemgleichungen eine spezifische Struktur aufweist. Eine ähnliche Herangehensweise wie beim I-Anteil ermöglicht die Schätzung und Rückführung der Störung, womit dieselben Regelungsziele verfolgt werden wie bei der Variante mit dem I-Anteil. Hier führt die dynamische Erweiterung mit dem Schätzer im Gegensatz zum I-Anteil allerdings wieder auf eine bilineare Systemgleichung. Allerdings ist dieser Ansatz weniger allgemein und erfordert eine Neuplanung der Referenztrajektorien in Echtzeit, birgt aber mehr Freiheiten in der Wahl der Reglerparameter für den geschlossenen Regelkreis. Als Rückführstrategie wird eine H∞-Zustandsregelung gewählt, um auftretenden Störungen mit möglichst minimalem Stellaufwand auszuregeln. Außerdem soll gleichzeitig der Fehler des Regelausgangs klein gehalten werden. Um schließlich die Stabilität des geschlossenen Regelkreises für nichtverschwindende Störungen untersuchen zu können, wird die sogenannten integral Input-to-State Stability (iISS) verwendet. Als Ergebnis der Arbeit können Bedingungen formuliert werden, wann eine suboptimale H∞-Zustandsregelung gefunden werden kann. Unter Annahme dieser Bedingungen folgt dann sofort die iISS-Eigenschaft des geschlossenen Regelkreises. Die Allgemeinheit des Verfahrens zeigt sich dadurch, dass es sogar möglich ist, den vorgestellten Ansatz auf allgemeine bilineare Systeme mit mehreren Eingängen zu erweitern. Das experimentelle Beispiel eines Hochsetzstellers in Kombination mit einem Gleichstrommotor wird dann zum Testen des Regelentwurfsverfahrens herangezogen. Dabei ist die Regelungsaufgabe, die Winkelgeschwindigkeit der Motorwelle einer vorgegeben Referenztrajektorie nachfahren zu lassen und auftretende Laststörungenauszuregeln. Dazu wurde die Variante der dynamischen Erweiterung anhand der Rückführung der Störung mit Trajektorienneuplanung verwendet. Mit einer suboptimalen H∞-Zustandsregelung wird der Regelkreis geschlossen, so dass iISS gewährleistet werden kann. Für die Echtzeitgenerierung der durch ein Approximationsverfahren ermöglichten Trajektorienneuplanung wird außerdem Beschränktheit gezeigt. Eine Vielzahl von Experimenten dient der genaueren Untersuchung des Verfahrens

Modeling and Large Signal Stability Analysis of A DC/AC Microgrid

abstract: The concept of the microgrid is widely studied and explored in both academic and industrial societies. The microgrid is a power system with distributed generations and loads, which is intentionally planned and can be disconnected from the main utility grid. Nowadays, various distributed power generations (wind resource, photovoltaic resource, etc.) are emerging to be significant power sources of the microgrid. This thesis focuses on the system structure of Photovoltaics (PV)-dominated microgrid, precisely modeling and stability analysis of the specific system. The grid-connected mode microgrid is considered, and system control objectives are: PV panel is working at the maximum power point (MPP), the DC link voltage is regulated at a desired value, and the grid side current is also controlled in phase with grid voltage. To simulate the real circuits of the whole system with high fidelity instead of doing real experiments, PLECS software is applied to construct the detailed model in chapter 2. Meanwhile, a Simulink mathematical model of the microgrid system is developed in chapter 3 for faster simulation and energy management analysis. Simulation results of both the PLECS model and Simulink model are matched with the expectations. Next chapter talks about state space models of different power stages for stability analysis utilization. Finally, the large signal stability analysis of a grid-connected inverter, which is based on cascaded control of both DC link voltage and grid side current is discussed. The large signal stability analysis presented in this thesis is mainly focused on the impact of the inductor and capacitor capacity and the controller parameters on the DC link stability region. A dynamic model with the cascaded control logic is proposed. One Lyapunov large-signal stability analysis tool is applied to derive the domain of attraction, which is the asymptotic stability region. Results show that both the DC side capacitor and the inductor of grid side filter can significantly influence the stability region of the DC link voltage. PLECS simulation models developed for the microgrid system are applied to verify the stability regions estimated from the Lyapunov large signal analysis method.Dissertation/ThesisMasters Thesis Engineering 201

MATLAB

This excellent book represents the final part of three-volumes regarding MATLAB-based applications in almost every branch of science. The book consists of 19 excellent, insightful articles and the readers will find the results very useful to their work. In particular, the book consists of three parts, the first one is devoted to mathematical methods in the applied sciences by using MATLAB, the second is devoted to MATLAB applications of general interest and the third one discusses MATLAB for educational purposes. This collection of high quality articles, refers to a large range of professional fields and can be used for science as well as for various educational purposes

Modelling & analysis of hybrid dynamic systems using a bond graph approach

Hybrid models are those containing continuous and discontinuous behaviour. In constructing dynamic systems models, it is frequently desirable to abstract rapidly changing, highly nonlinear behaviour to a discontinuity. Bond graphs lend themselves to systems modelling by being multi-disciplinary and reflecting the physics of the system. One advantage is that they can produce a mathematical model in a form that simulates quickly and efficiently. Hybrid bond graphs are a logical development which could further improve speed and efficiency. A range of hybrid bond graph forms have been proposed which are suitable for either simulation or further analysis, but not both. None have reached common usage. A Hybrid bond graph method is proposed here which is suitable for simulation as well as providing engineering insight through analysis. This new method features a distinction between structural and parametric switching. The controlled junction is used for the former, and gives rise to dynamic causality. A controlled element is developed for the latter. Dynamic causality is unconstrained so as to aid insight, and a new notation is proposed. The junction structure matrix for the hybrid bond graph features Boolean terms to reflect the controlled junctions in the graph structure. This hybrid JSM is used to generate a mixed-Boolean state equation. When storage elements are in dynamic causality, the resulting system equation is implicit. The focus of this thesis is the exploitation of the model. The implicit form enables application of matrix-rank criteria from control theory, and control properties can be seen in the structure and causal assignment. An impulsive mode may occur when storage elements are in dynamic causality, but otherwise there are no energy losses associated with commutation because this method dictates the way discontinuities are abstracted. The main contribution is therefore a Hybrid Bond Graph which reflects the physics of commutating systems and offers engineering insight through the choice of controlled elements and dynamic causality. It generates a unique, implicit, mixed-Boolean system equation, describing all modes of operation. This form is suitable for both simulation and analysis

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi