Basic sets and attractors of a double swing power system

In a normal power system, many generators are operating in synchrony. That is, they all have the same speed or frequency, a system frequency. In the case of an accident a situation might occur when one or more generators are running at a different speed, at much faster than the system frequency. They are said to be stepping out. We have been engaged in a series of studies of this situation, and have found global attractor-basin portraits. The electric power system involving one generator operating into an infinite bus is a well-established model with a long history of research. We, however, have derived a new mathematical model, in which there is no infinite bus, nor fixed system frequency. In the simple case of two subsystems (each a swing pair) weakly coupled by an interconnecting transmission line, we have developed a system of seven differential equations, which include the variation of frequency in a fundamental way. We then go on to study the behavior of this model, using the straddle orbit method of computer simulation to find the basic set. We succeed in finding many basic sets in this new model. In addition, we consider unstable limit sets which have two- or three-dimensional outset

Invariant Sets in Quasiperiodically Forced Dynamical Systems

This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of the existing theory for measure-preserving maps. The ergodic partition result is based on eigenspace at eigenvalue 0 of the associated Koopman operator, which is realized via time-averages of observables, and provides a constructive way to visualize a low-dimensional slice through a high-dimensional invariant set. We apply the result to the systems with a finite number of attractors and show that the time-average of a continuous observable is well-defined and reveals the invariant sets, namely, a finite number of basins of attraction. We provide a characterization of invariant sets in the quasiperiodically forced systems. A theoretical result on uniform boundedness of the invariant sets is presented. The series of theoretical results enables numerical analysis of invariant sets in the quasiperiodically forced systems based on the ergodic partition and time-averages. Using this, we analyze a nonlinear model of complex power grids that represents the short-term swing instability, named the coherent swing instability. We show that our theoretical results can be used to understand stability regions in such complex systems.Comment: 23 pages, 4 figure

Nonlinear dynamics in the flexible shaft rotating–lifting system of silicon crystal puller using Czochralski method

Acknowledgements The project is supported by the Key Program of National Natural Science Foundation of China (Grant No. 61533014).Peer reviewedPreprintPostprin

Basic sets and attractors of a double swing power system

In a normal power system, many generators are operating in synchrony. That is, they all have the same speed or frequency, a system frequency. In the case of an accident a situation might occur when one or more generators are running at a different speed, at much faster than the system frequency. They are said to be stepping out. We have been engaged in a series of studies of this situation, and have found global attractor-basin portraits. The electric power system involving one generator operating into an infinite bus is a well-established model with a long history of research. We, however, have derived a new mathematical model, in which there is no infinite bus, nor fixed system frequency. In the simple case of two subsystems (each a swing pair) weakly coupled by an interconnecting transmission line, we have developed a system of seven differential equations, which include the variation of frequency in a fundamental way. We then go on to study the behavior of this model, using the straddle orbit method of computer simulation to find the basic set. We succeed in finding many basic sets in this new model. In addition, we consider unstable limit sets which have two- or three-dimensional outset

Bifurcation, chaos, and voltage collapse in power systems

A model of a power system with load dynamics is studied by investigating qualitative changes in its behavior as the reactive power demand at a load bus is increased. In addition to the saddle node bifurcation often associated with voltage collapse, the system exhibits sub- and supercritical Hopf bifurcations, cyclic fold bifurcation, and period doubling bifurcation. Cascades of period doubling bifurcations terminate in chaotic invariant sets. The presence of these new bifurcations motivates a reexamination of the saddle-node bifurcation as the boundary of the feasible set of power injections.published_or_final_versio

Adaptive motion synthesis and motor invariant theory.

Generating natural-looking motion for virtual characters is a challenging research topic. It becomes even harder when adapting synthesized motion to interact with the environment. Current methods are tedious to use, computationally expensive and fail to capture natural looking features. These difficulties seem to suggest that artificial control techniques are inferior to their natural counterparts. Recent advances in biology research point to a new motor control principle: utilizing the natural dynamics. The interaction of body and environment forms some patterns, which work as primary elements for the motion repertoire: Motion Primitives. These elements serve as templates, tweaked by the neural system to satisfy environmental constraints or motion purposes. Complex motions are synthesized by connecting motion primitives together, just like connecting alphabets to form sentences. Based on such ideas, this thesis proposes a new dynamic motion synthesis method. A key contribution is the insight into dynamic reason behind motion primitives: template motions are stable and energy efficient. When synthesizing motions from templates, valuable properties like stability and efficiency should be perfectly preserved. The mathematical formalization of this idea is the Motor Invariant Theory and the preserved properties are motor invariant In the process of conceptualization, newmathematical tools are introduced to the research topic. The Invariant Theory, especially mathematical concepts of equivalence and symmetry, plays a crucial role. Motion adaptation is mathematically modelled as topological conjugacy: a transformation which maintains the topology and results in an analogous system. The Neural Oscillator and Symmetry Preserving Transformations are proposed for their computational efficiency. Even without reference motion data, this approach produces natural looking motion in real-time. Also the new motor invariant theory might shed light on the long time perception problem in biological research

Bistable energy harvesting backpack:Design, modeling, and experiments

Inspired by the dynamics of the noninertial systems, a novel bistable energy harvesting backpack is proposed that improves biomechanical energy harvesting performance. In contrast to traditional bistable energy harvesters that use an oblique compressed spring, a new bistable backpack is developed that uses the change of a spring torque direction located on a pinion. A detailed nondimensionalized model of the novel bistable energy harvesting backpack is developed and analyzed. Based on the dynamic bistable model, the influence of the carried backpack mass on the symmetry and the bifurcation frequency and amplitude of oscillation is examined to determine the ideal design parameters of the bistable backpack for experimental analysis and prototype manufacture. A comparison is made between the new bistable backpack and a traditional linear backpack under both harmonic and human walking excitation. The new bistable backpack design exhibits an improved frequency bandwidth from 1 Hz to 1.65 Hz at the base harmonic excitation of 2 m/s2 and the harvesting performance is enhanced from 2.34 W to 3.32 W when the walking speed is 5.6 km/h. The bench and treadmill tests verify the theoretical analysis and demonstrate the ability of the bistable energy harvesting backpack for broadband and performance enhancement.</p

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue