强迫Duffing振动系统的主共振鞍结分岔控制

设计了非线性参数控制器来改变非线性系统的稳态响应，减小了系统的响应幅值并消除了共振时的鞍结分岔。首先由多尺度法得到系统的近似频响方程，再由奇异性理论来分析分岔特性，从而实现非线性控制的目标。最后对强迫Duffing系统的主共振形式进行了分析，由数值模拟来确定分岔控制是可行的和有效的。     

Creep failure of a simply supported beam through a uniaxial Continuum Damage Mechanics model

Summary Creep failure of elastic-damageable beams is investigated using a simple Continuum Damage Mechanics model. A single-degree-of-freedom system is first studied for the bending problem of the visco-damage spring. The strong analogy between the behavior of such a system and the one of an imperfection sensitive viscoelastic column, with specific references to the buckling of columns is shown. In particular, the saddle-node bifurcation is clearly recognized in the bifurcation diagram. Large displacement analysis is considered when the true collapse mode is studied. The continuous beam is then studied with a local damage constitutive law. It is shown that the evolution problem, composed of a loading range and the creep test, is well posed for this statically determinate beam. It appears that it is not necessary to introduce some non-locality in the constitutive law, in order to regularize the evolution problem. The stability analysis at the structural level leads to a similar conclusion. There is a limit point in the bifurcation diagram (which is a functional space for this continuous problem). This limit point is obtained via analytical arguments. The limit load depends on the geometrical and material characteristics of the problem but does not depend on the viscosity of the local constitutive law. Numerical simulations illustrate the collapse mode.     

Optimal reactive power dispatch in a large power system with ac?dc and facts controllers

With the increased loading of existing power system, the problem of voltage stability and voltage collapse has become a major concern in power system planning and operation. The dependence of the system voltage profile on reactive power distribution forms the basis for reactive power optimisation. The technique attempts to utilises fully the reactive power sources in the system to improve the voltage profile and also to meet the reactive power requirements at the AC-DC terminals to facilitate the smooth operation of DC links. The method involves successive solution of steady-state power flows and optimisation of reactive power control variables with unified power flow controllers using linear programming technique. The proposed method has been tested on a real life equivalent 96-bus AC and a two terminal DC system.     

一类电力系统的分岔和奇异性分析

研究了单机无穷大系统在外部周期性激励负荷扰动作用下的非线性动力学行为：运用多尺度法分析了单机无穷大系统主共振的解析解及其稳定性,根据系统的分岔方程,运用C-L方法分析了主共振响应在不同系统参数下的不同分岔模式,研究表明该系统的不同分岔模式与其运行参数和结构参数有密切联系;数值仿真表明随着激励幅值的变化,该系统具有由倍周期分岔通往混沌直至增幅振荡失步的丰富动力学行为,从而为电力系统中同步发电机的同步运行、振荡失步提供理论指导。     

An isolated saddle-node bifurcation occurring inside a horseshoe

In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation ' inside ' a non-trivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is ' isolated ', that is, hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover, we construct a C 2 -open set of arcs having the same property.     

直线运动柔性梁非线性动力学--主参数共振与内共振联合激励

针对基础直线运动柔性梁，基于Kane方程建立了相应的非线性动力学方程。采用多尺度法并结合笛卡尔坐标变换，导出了系统受前两阶模态间3：1内共振及第二阶模态主参激共振时的非线性调制方程组．数值求解了该方程组的定常解及相应的稳定性问题。研究表明，系统的平凡、单模态、双模态稳态解共存，超临界及亚临界叉形分岔只发生在单模态状态下，相反，鞍结分岔及Hopf分岔只在双模态状态下产生，一些稳定的极限环随参数变化经一系列倍周期分岔后导致运动的突然跳跃。     

Reactive power/voltage control in distribution systems under uncertain environment

A novel method for reactive power/voltage control in distribution systems under uncertain data environment is presented. This is achieved by minimising boundary real power loss or boundary total real power demand while satisfying constraints on boundary bus voltage magnitudes. Such an approach is more realistic and intuitively satisfying as compared with the crisp solution with deterministic data assumption. On-load tap changing facility of the transformer at the substation and the shunt capacitors at the substation and feeders are used as control variables. A truly nonlinear fuzzy distribution power flow is used, in which simultaneous non-statistical uncertainties in load forecast, load model coefficients and network parameters are incorporated. Genetic algorithm is used to solve the problem. In order to demonstrate the effectiveness of the proposed method, results for balanced 30-bus and unbalanced 25-bus and modified 123-bus systems have been obtained.     

Intelligent energy management control for independent microgrid

This work presents a new adaptive scheme for energy management in an independent microgrid. The proposed energy management system has been developed to manage the utilization of power among the hybrid resources and energy storage system in order to supply the load requirement based on multi-agent system (MAS) concept and predicted renewable powers and load powers. Auto regressive moving average models have been developed for predicting the wind speed, atmospheric temperature, irradiation, and connected loads. The structure proposed in this paper includes renewable sources as primary source and storage system as secondary source. A wind generator and solar PV array system together acts as primary source, which supplies power to the local load most of the time in this energy management strategy. When they fail to meet the load demand, the secondary source present in the system will assist the primary source and help to attain the goal of satisfying load demand without interruption. If the primary source and secondary source together are not able to meet the load demand then load shedding will be executed according to the priority set. Thus the developed MAS algorithm co-ordinates the hybrid system components and achieves energy management among renewable energy sources, storage units, and load under varying environmental conditions and varying loads. STATCOM based compensation has been implemented to balance the reactive power demand and to mitigate the voltage fluctuations and harmonics on the AC bus. The proposed microgrid has been simulated with MAS concept in Matlab/Simulink environment. The results presented in this paper show cases the effectiveness of the proposed energy management controller.     

Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: the zipper

Using numerical continuation we show a new bifurcation scenario involving resonant periodic orbits in a parametrized four-dimensional autonomous system deriving from nonlinear rotordynamics. The scenario consists of a carefully orchestrated sequence of transcritical bifurcations in which branches of periodic solutions are exchanged. Collectively, the bifurcations resemble the action of a zipper. An underlying governing mechanism clearly exists but still has to be uncovered. For a range of parameter values the sequence of bifurcations forms a global connection between a Sil'nikov bifurcation and (partial) mode-locking. The homoclinic bifurcation is introduced into the system by a Takens-Bogdanov bifurcation. The system also features an interaction between two chaotic Sil'nikov bifurcations.     

Singular perturbations for sensitivity analysis in symmetric bifurcation buckling

A direct procedure for the evaluation of imperfection‐sensitivity in bifurcation problems is presented. The problems arise in the context of the general theory of elastic stability (Koiter's theory) for discrete structural systems, in which the total potential energy is employed together with a stability criterion based on energy derivatives. The imperfection sensitivity of critical states, such as bifurcations and trifurcations, is usually represented as a plot of the critical load versus the amplitude ε of the imperfection considered. However, such plots have a singularity at the point with ε=0, so that a regular perturbation expansion of the solution is not possible. In this work, we describe a direct procedure to obtain the sensitivity of the critical load (eigenvalue of the bifurcation problem) and the sensitivity of the critical direction (eigenvector of the bifurcation problem) using singular perturbation analysis. The perturbation expansions are constructed as a power series in terms of the imperfection amplitude, in which the exponents and the coefficients are the unknowns of the problem. The solution of the exponents is obtained by means of trial and error using a least degenerate criterion, or by geometrical considerations. To compute the coefficients a detailed formulation is presented, which employs the conditions of equilibrium and stability at the critical state and their contracted forms. The formulation is applied to symmetric bifurcations, and the coefficients are solved up to third‐order terms in the expansion. The algorithmis illustrated by means of a simple example (a beam on an elastic foundation under axial load) for which the coefficients are computed and the imperfection‐sensitivity is plotted. Copyright © 2001 John Wiley & Sons, Ltd.     

Reactive power transfer allocation method with the application of artificial neural network

A novel method to identify the reactive power transfer between generators and load using modified nodal equations is proposed. On the basis of the solved load flow results, the method partitions the Y-bus matrix to decompose the current of the load buses as a function of the generators' current and voltage. Then it uses the load voltages from the load flow results and decomposed load currents to determine reactive power contribution from each generator to loads. The validation of the proposed methodology is demonstrated by using a simple 3-bus system and the 25-bus equivalent system of south Malaysia. Next part here focuses on creating an appropriate artificial neural network (ANN) to solve the same problem in a simpler and faster manner. The basic idea is to use supervised learning paradigm to train the ANN. Most commonly used feedforward architecture has been chosen for the proposed ANN reactive power transfer allocation technique. Almost all system variables obtained from load flow solutions are utilised as an input to the neural network. Moreover, tan-sigmoid activation functions are incorporated in the hidden layer to realise the nonlinear nature of the reactive power transfer allocation. The targets of the ANN corresponding to the previously developed reactive power transfer allocation method. The 25-bus equivalent system of south Malaysia is utilised as a test system to illustrate the effectiveness of the ANN output compared with that of the modified nodal equations method. The ANN output provides promising results in terms of accuracy and computation time.     

Smart demand for improving short-term voltage control on distribution networks

Smart grids must involve active roles from end users in order to be truly smart. The energy consumption has to be done in a flexible and intelligent manner, in accordance with the current conditions of the power system. Moreover, with the advent of dispersed and renewable generation, increasing customer integration to aid power system performance is almost inevitable. This study introduces a new type of smart demand side technology, denoted demand as voltage controlled reserve (DVR), to improve short-term voltage control, where customers are expected to play a more dynamic role to improve voltage control. The technology can be provided by thermostatically controlled loads as well as other types of load. This technology is proven to be effective in case of distribution systems with a large composition of induction motors, where the voltage presents a slow recovery characteristic due to deceleration of the motors during faults. This study presents detailed models, discussion and simulation tests to demonstrate the technical viability and effectiveness of the DVR technology for short-term voltage control.     

考虑压缩效应的简支弹性杆受压屈曲的理论分析

用奇异性理论研究轴向压缩以及由之引起的横截面积扩大对弹性压杆屈曲的影响。新模型得到的屈曲临界压力大于经典欧拉模型所给之值,且新模型显示,在无量纲特征长度的三个不同取值区间中,弹性杆的一阶屈曲模态表现为三种不同的形式:#x0201c;超临界叉式分支#x0201d;、#x0201c;亚临界叉式分支#x0201d;和#x0201c;不存在#x0201d;。而在经典欧拉模型中,弹性杆的一阶屈曲模态总表现为#x0201c;超临界叉式分支#x0201d;。根据新模型,定性评价了现有实验数据,并通过算例分析,解释了传统材料制作的杆件在较短时将发生屈服破坏而非亚临界叉式分支屈曲的现象。     

Dynamics, bifurcations and chaos in coupled lasers

Experiments and numerical modelling on two different class B lasers that are subjected to external optical light injection are presented. This presentation includes ways of measuring the changes in the laser output, how to numerically describe the systems and how to construct diagrams of the dynamical states in the plane frequency detuning between lasers and injection strength. The scenarios for the semiconductor laser include an area of frequency locking and islands of chaotic behaviour embedded in and mixed with periodic doubling regimes. Using a rate equation model, the largest Lyapunov exponent is calculated as a measure of the stability of equilibriums and the amount of chaos in chaotic regimes. In the solid-state laser case, different dynamical regions were clearly observed. The found boundaries were identified experimentally, using an identification method, and numerically, from bifurcation analysis, as Hopf, saddle-node, period-doubling and torus bifurcations.     

Conic programming approach for static voltage stability analysis in radial networks

That the problem of computing the capacity limit of a radial distribution system can be formulated as a second-order cone program is shown. The implications of the conic programming formulation are 2-fold. First, the load capability of the radial system can be obtained using existing efficient implementations of polynomial time interior-point algorithms, thus avoiding the need for running a sequence of load flow solutions. Secondly, the conic objective function yields a voltage stability indicator (SI). This indicator quantifies the maximum percentage by which the current load profile can be uniformly increased before voltage collapse occurs. The proposed method is validated by computing the load capability and voltage SIs of 11 different distribution systems. Comparisons are carried out with five previously published voltage SIs     

基于中心流形理论的小水电并网系统Hopf分岔分析

针对小水电并网系统,用Matcont软件搜寻系统的Hopf分岔点绘制分岔图;利用中心流形理论将高维电力系统降到二维模型,并通过计算二维模型分岔稳定性指标的正负判定原系统Hopf分岔类型。结果表明,分岔稳定性指标大于零时电压失稳,小于零时电压稳定。用Matlab软件对讨论结果进行数值仿真,证明理论结果的正确性。     

Field test of 70 MW class superconducting generator

Super-GM and the Kansai Electric Power Co., tested a 70 MW class model superconducting generator in actual power system. The model machine, operated as a rotary condenser, was connected to a 77 kV commercial power grid through 77/6.6 kV transformers. It supplied 40 MVar of leading reactive power to the electric power system. The model machine showed an ability to operate steadily through all the tests and various load changes in the commercial electric power system. The test results proved that the small synchronous reactance of the superconducting generator enhances voltage stabilization and their leading reactive capacity is larger, compared with conventional generators.     

壁板边界松驰下颤振非线性动力特性分析

采用分离变量法和伽辽金法建立三维壁板的非线性气动弹性运动方程,用一阶活塞理论模拟壁板所受的气动力,分析了壁板的颤振边界及稳定性,进而取边界松弛因子,动压和面内力为分叉参数,研究壁板颤振时的分叉及混沌等复杂动力学特性。计算结果表明：边界松弛下壁板颤振系统表现出丰富的动力学行为,其分叉特性很复杂。随着边界松弛因子的增大, 静态稳定区域缩小,而屈曲和混沌区域增大,系统稳定性降低。     

一类周期系数力学系统的Hopf-Flip分岔

研究了一类周期系数力学系统因周期运动失稳而产生Hopf-Flip分岔的问题.首先根据拉格朗日方程给出了该力学系统的运动微分方程,并确定其周期运动的具有周期系数的扰动运动微分方程,再根据周期系数系统的稳定性理论建立了其给定周期运动的Poincaré映射,进一步根据该系统的特征矩阵的特征值穿越单位圆情况分析判断该Poincaré映射不动点失稳后将发生Hopf-Flip分岔,并用数值计算加以验证.结果表明,非共振条件下,系统的周期运动可通过Hopf-Flip分岔,进而演变成次谐运动,而三阶强共振条件下系统周期运动失稳后形成不稳定的次谐运动.     

General sensitivity formulas for maximum loading conditions in power systems

General sensitivity formulas for maximum loading conditions of nonlinear power systems have been proposed. The proposed formulas allow computing the sensitivities of any system variable and, in particular, of the maximum loading margin with respect to arbitrary parameters. This approach extends previous results. It has also been shown that the sensitivity formulae available in the literature for static saddle-node and limit-induced bifurcation points are particular cases of the proposed general formulae. Two benchmark systems, namely a 6-bus system and the IEEE RTS-96 24-bus tests system, are used to illustrate and test the proposed technique