Robustness analysis for power systems based on the structured singular value tools and the [nu] gap metric

Modern power systems are operated more stressed than ever because of the advent of deregulation and competition. One of the important issues in the design of controllers for a stressed system is to evaluate the stability of the controlled system over a range of operating conditions.;The conventional controllers are designed to make the system stable under certain conditions of operation. The time consuming time domain simulation is then used to evaluate the controllers for a few selected operating conditions around which the controllers are designed. Such a design and evaluation procedure cannot guarantee robustness of the controller over the whole range of operating conditions.;In this dissertation, practical algorithms to perform robustness analysis based on two tools, structured singular value and the nu gap metric, are investigated. The power system stabilizer is used as the controller and small signal stability is of interest.;The robustness problem in the SSV framework is set up for the multimachine power system. In this formulation, an improved uncertainty characterization has been used to capture the effect of parameter variations in terms of the varying elements of the linearized system matries, which are derived from the component differential equations and the network algebraic equations separately. SVD decomposition is used to reduce the size of the problem. Based on the resulting framework, a branch and bound scheme is proposed to intelligently select frequency intervals on which the frequency sweep test can be performed further to find the peak of mu. Instead of blindly choosing frequency intervals to sweep, which could ignore important frequency points on the mu plots, this scheme provides searching under guidance. The analysis procedure accurately predicts the range of stable operating conditions which are verified by repeated eigenvalue analysis.;Fir the robustness in terms of nu gap metric, we set up the feedback configuration for multimachine power system. The frequency response of the nu gap metric is plotted and its relationship with that of the stability margin is used to determine the stability of the perturbed systems. A weighted nu gap metric is defined and its frequency domain interpretation is explored to further reduce the conservatism of the results.;Finally, a feedback configuration is carefully developed to carry out the McFarlane and Glover Hinfinity loop shaping design procedure. The effect of the damping controller on improving system dynamic performance is also examined.;Comparisons are made between the two major analysis tools via the results on the same test systems with the same scenarios

Angle rigidity and its usage to stabilize multi-agent formations in 2D

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multi-point framework, named "angularity", consisting of a set of nodes embedded in a Euclidean space and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame and are signed according to the counter-clockwise direction. Here angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient condit

Bearing rigidity and formation stabilization for multiple rigid bodies in SE(3)

In this work, we first distinguish different notions related to bearing rigidity in graph theory and then further investigate the formation stabilization problem for multiple rigid bodies. Different from many previous works on formation control using bearing rigidity, we do not require the use of a shared global coordinate system, which is enabled by extending bearing rigidity theory to multi-agent frameworks embedded in the three dimensional special Euclidean group SE(3) and expressing the needed bearing information in each agent's local coordinate system. Here, each agent is modeled by a rigid body with 3 DOFs in translation and 3 DOFs in rotation. One key step in our approach is to define the bearing rigidity matrix in SE(3) and construct the necessary and sufficient conditions for infinitesimal bearing rigidity. In the end, a gradient-based bearing formation control algorithm is proposed to stabilize formations of multiple rigid bodies in SE(3)

Stress analysis of rigid hanger of railway arch bridge based on vehicle-bridge coupling vibration

In order to study the stress of two new types of rigid hangers (circular steel and flat-plate rigid hangers) on the railway arch bridges, a finite element model of a railway through arch bridge was established. The influences of different types and sizes of hangers on the dynamic characteristics of the bridge were compared. Based on the established vehicle-bridge coupling vibration model, the influences of circular steel and flat-plate hanger sizes on the stress amplitude of hanger were discussed when the train passes through the bridge. The results show that when the flexible hanger of arch bridge was replaced by the rigid hanger, the symmetrical vertical bending frequency of bridge significantly increased. With the change of the size of flat-plate hanger, the torsional mode of the bridge was doped with the local vibration of the flat-plate hanger. With the increase of circular steel hanger diameter, the maximum stress amplitude of the hanger decreases as a whole. As for the flat-plate hanger, when the long side size b is the same, the maximum stress amplitude of the hanger decreases with the increase of the short side size d. When the short side size d is the same, with the increase of the long side size b, the maximum stress amplitude of the shorter hanger decreases, and the maximum stress amplitude of the longer hanger increases. When the size of the flat-plate hanger is too small or too large, the maximum stress amplitude is large