Aktuell unterliegt unsere Stromversorgung mit der Energiewende einer Transformation, welche letzten Endes auch Änderungen der Struktur des Stromnetzes bedingt. Jenes ist ein hochkomplexes System aus unzähligen Erzeugern und Verbrauchern die miteinander wechselwirken. Im Lichte dessen leiten sich, (nicht nur) für zukünftige Stromnetze, einige methodischen Fragen ab. Wie kann die Stabilität verschiedener Betriebszustände oder Szenarien miteinander verglichen werdem? Welches sind die neuralgischen Punkte eines Stromnetzes? Zu welchem Grad bestimmt die Netzwerkstruktur die Systemstabilität? Im Zentrum der vorliegenden Dissertation steht dabei das emergente Phänomen der Synchronisation in Oszillatornetzwerken sowie dessen Stabilität. Im Bezug auf Stromnetze ist die Synchronisation dadurch gekennzeichnet, dass alle Erzeuger und Verbraucher mit der Netzfrequenz im Takt schwingen. Mit probabilistischen Stabilitätsmaßen lässt sich die Systemstabilität auf verschiedene Art quantifizieren. Neben einer Untersuchung möglicher Beschränkungen werden zwei neue probabilistische Maße entwickelt. Dabei spielen insbesondere die Häufigkeit und Dauer von Störungen sowie die Einhaltung der Betriebsgrenzen eine Rolle. Weiterhin wird der Einfluss kleiner Netzwerkstrukturen, sogenannter Motive, auf die Stabilität herausgearbeitet. Hierzu werden die Stabilitätsmaße in statistischen Verfahren mit charakteristischen Größen aus der Netzwerktheorie verknüpft. Es zeigt sich dann, dass das Auftreten spezieller Motive die Systemstabilität erhöht, wohingegen andere diese herabsetzen. Diese Zusammenhänge zwischen Netzwerkmotiven und Stabilität der Synchronisation erweitern die Kenntnisse über Zusammenhänge zwischen Struktur und Stabilität komplexer Systeme. Darüber hinaus erweitern die neu entwickelten probabilistischen Stabilitätsmaße das Methodenspektrum der nichtlinearen Dynamik zur Stabilitätsanalyse, insbesondere für Systeme auf komplexen Netzwerken mit vielen Freiheitsgraden. / In the light of the energy transition, power systems undergo a major transformation enabled by appropriate modifications of the grid’s underlying structure. This network constitutes the complex interaction of numerous producers and consumers. The power grid is additionally subject to intermittent disturbances that also include large deviations. These aspects prompt methodological problems for (future) power grids in particular and complex systems in general. How can the stability of different operating points or scenarios be compared? What are the critical components of the network? To which extent is the stability of an operating point determined by the network structure? This dissertation focusses on the emergent phenomenon of synchronisation on networks. In power grids, this corresponds to all units working at the same rhythm – the rated grid frequency. Regarding an analysis with so-called probabilistic stability measures, important limitations are discussed and novel approaches are developed. In particular, the new measures consider repeated perturbations as well as operational bounds on transient deviations. Moreover, the influence of small network structures, so-called motifs, on the stability is investigated. For this purpose, the stability measures are paired with network characteristics using statistical approaches. On this basis, it turns out that, while the abundance of special motifs enhances stability, others typically diminish it. In conclusion, the development of analysis methods and their comparison with network characteristics uncovers relationships between network motifs and the stability of synchronisation. These results are general to a large class of complex systems and build a foundation to future research in this direction. In addition to that, the novel probabilistic stability measures extend the range of methods in nonlinear dynamics by important aspects, especially for high-dimensional complex systems.

The grid-connected photo-voltaic (PV) system is one of the most promising renewable energy solutions which offers many benefits to both the end user and the utility network and thus it has gained the popularity over the last few decades. However, due to the very nature of its invariability and weather dependencies, the large scale integration of this type of distributed generation has created challenges for the network operator while maintaining the quality of the power supply and also for reliable and safe operations of the grids. In this study, the behavioral impact of large scale PV system integration which are both steady and dynamic in nature was studied.  An aggregate PV model suited to study the impacts was built using MATLAB/Simulink.  The integration impacts of PV power to existing grids were studied with focus on the low voltage residential distribution grids of Mälarenergi Elnät AB (10/0.4 kV). The steady state impacts were related to voltage profile, network loss. It was found that the PV generation at the load end undisputedly improves the voltage profile of the grid especially for the load buses which are situated at farther end of the grid. Further, with regard to the overvoltage issue, which is generally a concern during the low load demand period it was concluded that, at a 50% PV penetration level, the voltage level for the load buses is within the limit of 103% as prescribed by the regulator excepting for few load buses. The voltage level for load buses which deviate from the regulatory requirement are located at distance of 1200 meter or further away from the substation. The dynamic impact studied were for voltage unbalancing in the grid, which was found to have greater impact at the load buses which is located farther compared to a bus located nearer to the substation. With respect to impact study related to introduction of harmonics to the grid due to PV system integration, it was found that amount of harmonic content which was measured as total harmonic distortion (THD) multiplies with integration of more number of PV system. For a 50 % penetration level of PV, the introduced harmonics into the representative network is very minimal. Also, it was observed from the simulation study that THD content are be less when the grid operates at low load condition with high solar irradiance compared to lower irradiance and high load condition.