Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters

The Impact of Renewable Power Generation and Extreme Weather Events on the Stability and Resilience of AC Power Grids

Der erste Teil dieser Arbeit beschäftigt sich mit der Frage, welchen Einfluss kurzzeitige Schwankungen der erneuerbaren Energiequellen auf die synchrone Netzfrequenz haben. Zu diesem Zweck wird eine lineare Antworttheorie für stochastische Störungen von dynamischen Systemen auf Netzwerken hergeleitet. Anschließend wird diese Theorie verwendet, um den Einfluss von kurzfristigen Wind- und Sonnenschwankungen auf die Netzdynamik zu analysieren. Hierbei wird gezeigt, dass die Frequenzantwort des Netzes weitestgehend homogen ist, aber die Anfälligkeit für Leistungsschwankungen aufgrund von Leitungsverlusten entlang des Leistungsflusses zunimmt. Der zweite Teil der Arbeit befasst sich mit der Modellierung von netzbildenden Wechselrichterregelungen. Bislang existiert kein universelles Modell zur Beschreibung der kollektiven Dynamik solcher Systeme. Um dies zu erreichen, wird unter Ausnutzung der inhärenten Symmetrie des synchronen Betriebszustandes eine Normalform für netzbildende Akteure abgeleitet. Anschließend wird gezeigt, dass dieses Modell eine gute Annäherung an typische Wechselrichter-Dynamiken bietet, aber auch für eine datengesteuerte Modellierung gut geeignet ist. Der letzte Teil der Arbeit befasst sich mit der Analyse des Risikos von Stromausfällen, welche durch Hurrikans verursacht werden. Hohe Windgeschwindigkeiten verursachen häufig Schäden an der Übertragungsinfrastruktur, welche wiederum zu Überlastungen anderer Komponenten führen und damit eine Kaskade von Ausfällen im gesamten Netz auslösen können. Simulationen solcher Szenarien werden durch die Kombination eines meteorologischen Windmodells sowie eines Modells für kaskadierende Leitungsausfälle durchgeführt. Durch Monte-Carlo-Simulationen in einer synthetischen Nachbildung des texanischen Übertragungsnetzes können einzelne kritische Leitungen identifiziert werden, welche zu großflächigen Stromausfällen führen.The first part of this thesis addresses the question which impact short-term renewable fluctuations have on the synchronous grid frequency. For this purpose, a linear response theory for stochastic perturbations of networked dynamical systems is derived. This theory is then used to analyze the impact of short-term wind and solar fluctuations on the grid frequency. It is shown that while the network frequency response is mainly homogenous, the susceptibility to power fluctuations is increasing along the power flow due to transmission line losses. The second part of the thesis is concerned with modeling grid-forming inverter controls. So far there exists no universal model for studying the collective dynamics of such systems. By utilizing the inherent symmetry of the synchronous operating state, a normal form for grid-forming actors is derived. It is shown that this model provides a useful approximation of certain inverter control dynamics but is also well-suited for a data-driven modeling approach. The last part of the thesis deals with analyzing the risk of hurricane-induced power outages. High wind speeds often cause damage to transmission infrastructure which can lead to overloads of other components and thereby induce a cascade of failures spreading through the entire grid. Simulations of such scenarios are implemented by combining a meteorological wind field model with a model for cascading line failures. Using Monte Carlo simulations in a synthetic test case resembling the Texas transmission system, it is possible to identify critical lines that trigger large-scale power outages

Advanced Inverter control for mixed source microgrids

This thesis focuses on investigating virtual oscillator control (VOC) and applying it to mixed source microgrids to address several stability issues. A detailed comparison between VOC and droop control in a three-phase system is presented in terms of transient responses of a single inverter under small load disturbances and the synchronization speed in multiple paralleled inverters under various inverter terminal voltage amplitude and frequency regulation settings. In the single-inverter microgrid, it is demonstrated in both simulation and experiment that the two control models produce similar transient responses in the output voltage and current amplitudes. However, VOC has a faster instantaneous frequency transient response whilst still maintaining the terminal voltage amplitude transient response of the droop controller. In microgrids with multiple inverters, the synchronization speed of the VOC is faster than that of the droop control when the terminal voltage’s frequency regulation range is allowed to be wide. The conclusion is verified with different types of loads. A virtual inertia design method for the VOC inverter with a mixed source microgrid is presented to improve the frequency stability issues of the system. The per unit inertia constant of a VOC inverter is derived when coupled with a synchronous generator in an islanded microgrid. The control parameters of the virtual inertia are designed via small-signal analysis. A dual second order generalized integrator - frequency locked loop (DSOGI-FLL) is adopted for digital implementation of proposed virtual inertia based VOC. With the use of virtual inertia block, the frequency nadir is improved by 22% and rate of change of frequency is improved by 29% compared with the unmodified VOC inverter during the transient period induced by load disturbances. Simulation and experimental results verify the enhanced transient response of system frequency. A voltage and current dual-loop control structure is added to the VOC inverter to solve the voltage drop issues at the inverter terminals caused by the inverter dead-time effects, non-ideal semiconductor and LCL filter. A complete small-signal model for a multiple-inverters microgrid with the proposed control structure is presented in order to assess system stability using eigenvalue and participation factor analysis. Analytical results show that the parameter related to the frequency regulation and the integral gain of the voltage controller affect the location of the system’s dominant modes significantly. The stability margin is determined by modifying these control parameters. Experimental results on a laboratory test microgrid verify the predication from the small-signal analysis and time-domain simulations. Finally, a method to limit current in the VOC inverter under large disturbances in a mixed source microgrid is proposed. During a large load change in the islanded microgrid, the inverter based sources may get temporarily overloaded until other generations with sufficient power margin take the remaining load burden. The original VOC inverter lacks the ability to constrain the current within limits during the transient period. The dual-loop structure proposed in this thesis can limit the transient current with the use of virtual impedance. Such virtual impedance is presented by the desired maximum current magnitude and virtual voltage drop. Compared with a recently proposed fault ride through VOC inverter, the proposed virtual impedance based current limitation method can effectively constrain the inverter current within the pre-set value under large disturbances, which augments the range of application of VOC and enhances its robustness