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Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
This chapter provides an introduction to the modeling and control of power generation from wind turbine systems. In modeling, the focus is on the electrical components: electrical machine (e.g. permanent-magnet synchronous generators),…
Ever-growing electrical loads are having a huge impact on the operation and stability of the power system. Moreover, the integration of renewable generation poses various challenges to the future power system, especially, regarding…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for large-…
This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat…
Rotational inertia is stabilizing the frequency of electric power systems against small and large disturbances, but it is also the cause for oscillations between generators. As more and more conventional generators are replaced by renewable…
The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of…
Synchronization is an essential element in three-phase ac electric power systems. The large-scale integration of converter-interfaced resources leads to the power grid transformation from voltage-source-dominated to…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
The expansion of inverter-connected generation facilities (i.e. wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change. Whereas conventional generation with large rotating…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
Large-scale integration of inverter-based resources into power grids worldwide is challenging their stability and security. This paper takes a closer look at synchronous condensers as a solution to mitigate stability challenges caused by…
We analyze in this paper the effect of the well known intelligent proportional controller on the stability of linear control systems. Inspired by the literature on neutral time delay systems and advanced type systems, we derive sufficient…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
Vortex solutions in the two Higgs doublet electroweak model are constructed, and their stability to small perturbations is studied. The most general perturbation is decomposed into angular momentum modes, the least stable mode is…
Stability of power grids with synchronous generators (SGs) and renewable generation interfaced with grid-forming converters (GFCs) under dc-side current limitation is studied. To that end, we first consider a simple 2-bus test system and…
Increasing the inertia is widely considered to be the solution to resolving unstable interactions between coupled oscillators. In power grids, Virtual Synchronous Generators (VSGs) are proposed to compensate the reducing inertia as rotating…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…