Analysis of complex intermittency in Boost converter from a bifurcation control viewpoint

Due to undesirable interference via unintended coupling paths, switching converters may exhibit complex intermittency, which appears as a form of bifurcation undergoing regular operation, subharmonics, and chaos orderly and repeatedly for a long period of time. Such intermittent operation, being an unwanted operating state, should normally be avoided in power converters. This paper expounds the mechanism and conditions for the emergence of intermittency in a common current-mode controlled Boost converter. It is found that interference at frequencies near the switching frequency or its rational multiples may induce intermittent operation. The strengths and frequencies of the interfering signals determine the type and period of intermittency. The problem is analyzed by transforming the time-bifurcation analysis to a conventional parameter-bifurcation analysis. Based on this transformation, intermittency can be investigated from the bifurcation control viewpoint. Furthermore, the critical circuit parameter conditions for the emergence of intermittency can be predicted and compared with those from circuit simulation.

Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance （IHB） and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated postregulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.

Intermittency and bifurcation in SEPICs under voltage-mode control

A stroboscopic map for voltage-controlled single ended primary inductor converter （SEPIC） with pulse width modulation （PWM） is presented, where low-frequency oscillating phenomena such as quasi-periodic and intermittent quasi-periodic bifurcations occurring in the system are captured by numerical and experimental methods. According to bifurcation diagrams and nonlinear dynamical theory, the characteristics of the low-frequency oscillation and the mechanism for the appearance of the low-frequency oscillation are investigated. It is shown that as the controller parameter varies, the change in the conduction mode takes place from the continuous conduction mode （CCM） under the originally stable period one and high periodic orbits to the intermittent changes between CCM and discontinuous conduction mode （DCM）, which may be related to the losing stability of the system and brought the system to exhibiting low-frequency oscillating behaviour in the time domain. Moreover, the occurrence of the intermittent quasi-periodic oscillation reflects that the system undergoes a Neimark-Sacker bifurcation.

Study on Bifurcation and Chaos in Boost Converter Based on Energy Balance Model

Based on boost converter operating in discontinuous mode, this paper proposes an energy balance model (EBM) for analyzing bifurcation and chaos phenomena of capacitor energy and output voltage when the converter parameter is varying. It is found that the capacitor energy and output voltage dynamic behaviors exhibit the typical period-doubling route to chaos by increasing the feedback gain constant K of proportional controller. The accurate position of the first bifurcation point and the iterative diagram of the capacitor energy with every K can be derived from EBM. Finally, the underlying causes for bifurcations and chaos of a general class of nonlinear systems such as power converters are analyzed from the energy balance viewpoint. Com-paring with the discrete iterative model, EBM is simple and high accuracy. This model can be easily devel-oped on the nonlinear study of the other converters.

Analysis of grid-connected voltage stability of FSCWT based on bifurcation theory

This paper studies on the change mechanisms of the voltage stability caused by the grid connection of front-end speed-controlled wind turbines(FSCWT)integrating into power system.First of all,the differential algebraic equations describing the dynamic characteristics of wind turbines are illustrated.Then,under the guidance of IEEE3 node system model,the influence of the angular velocity of wind turbines,the reactive power and the active power at load bus on the voltage stability of grid-connection has been analyzed by using bifurcation theory.Finally,the method of linear-state feedback control has been applied to the original system in accordance with the bifurcation phenomenon of grid-connected voltage caused by the increase in the active power at load bus.Research shows that voltage at the grid-connected point would be changed with the fluctuation of turbines angular velocity.And increasing its reactive power can enhance voltage at the grid-connected point;problem of bifurcation at the grid-connected point can be delayed when increasing the gain k s of feedback controller within a certain range.

Intermittency in Switching Power Converters:Theoretical Analysis

In view of reasonable explanation of intermittent subharmonics and chaos that can be gained from coupling filter between circuits,this paper discusses a method that maps time bifurcation with parameter bifurcation.Based on this mapping method,the general analysis method of characteristic multiplier,which is originally aimed at parameter bifurcation,can be used for the study of intermittency,i.e.,time bifurcation.In this paper,all researches coming from characteristic multipliers,parameter-bifurcation diagrams,and the largest Lyapunov exponent indicate the same results as those produced by simulation and experiment.Thus,it is proved theoretically that the intermittency in switching power converter can be explained in terms of coupling of spurious interference.

Dynamical Behavior of V^2C Control Boost Converter

A discrete iterative map model of V^2C control boost converter was established to study the dynamical behaviors of the converter. By using parameter space map and bifurcation diagram, the effects of circuit parameters on the bifurcation behaviors of V^2C control and current-mode control boost converters were analyzed. The phase portraits and time-domain waveforms of the V^2C control boost converter were obtained by Runge-Kutta algorithm through piecewise smooth switching model. The research results indicate that V^2C control boost converters can evolve into periodic and chaotic behaviors, and show weaker nonlinear behaviors than current-mode control boost converters.

Control of Instable Chaotic Small Power System

In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned power system by means of modern nonlinear theory (Bifurcation and Chaos). Our model is based on a three bus power system that consists of multi generators containing both dynamic and static loads. They are considered to be in the form of an induction motor in parallel with a capacitor, as well as a combination of constant power along with load impedance, PQ. We consider the load reactive power as the control parameter. At this stage, after changing the control parameter, the study showed that the system is experiencing a subcritical Hopf bifurcation point. This leads to a chaos within the system period doubling path. We then discuss the system controllability and present that the all chaotic oscillations fade away through the linear controller that we impose on the system.

流控型Buck变换器的动力学行为分析

针对光伏发电系统中电流控制型Buck变换器,利用不连续动力学理论分析了其非线性振荡行为.通过调节控制电路的电压幅值和直流激励电源值,给出碰撞边界的和时钟脉冲触发的参数分岔图,获得了电流控制型Buck变换器从稳定的周期1到混沌状态的参数节点.分别绘制周期和混沌运动的相轨迹和时序图,分析各子域内具有不同映射结构的系统类型.研究结果表明,流控制型Buck变换器在参数变化时其运动行为丰富,边界碰撞现象明显,观测到倍周期分岔和阵发混沌.通过分析映射类型,说明其边界的非线性振荡行为.

低电压穿越控制诱导的陆上风电场电压振荡的分岔分析及其判据研究

集中送出的陆上风电场电压支撑能力弱,且有功送电距离大多较长,随着其有功出力的增加,其电压稳定问题不可忽视。在实际电网中,曾出现过陆上风电场在高出力、无故障下、低电压穿越控制方式导致的电压振荡失稳现象,该文基于简化模型,针对该现象进行机理分析,并引申出适用于多机系统的判据。在机理分析方面,说明其对应一种高出力下低电压穿越控制诱导的非光滑分岔(high output excited low voltage ride through control induced non-smooth bifurcation,HLINB),并分析了HLINB与鞍结分岔(saddle node bifurcation,SNB)发生的边界条件;在判据方面,给出了发生HLINB的判据,并结合二阶锥算法给出判据的阈值计算方法。具体地,首先,基于实际案例,对陆上风电场无故障、高出力下,由低穿控制方式导致的电压振荡现象进行分析,说明该振荡现象对应于HLINB,进一步,推导HLINB与SNB发生的边界条件,结果表明,在风电场的典型低穿控制方式下,陆上风电场在高出力时更容易发生HLINB而非SNB;其次,分析了其他风电场无功控制方式对于待评估风电场的最大输出功率的影响,并基于二阶锥算法,给出考虑风电场无功控制方式及无功约束下,计及HLINB约束的风电场的最大输出功率的计算方法;最后,3机9节点和10机39节点的仿真算例表明,所提方法考虑风电场的控制方式,能够更加有效的评估系统的电压稳定性。

基于Buck变换器的模糊自抗扰Hopf分岔扰动抑制策略

针对Buck变换器输出端口电压易受系统参数变化影响而降低能量传输质量的问题,提出了一种结合模糊推理机制的线性自抗扰控制策略。首先,建立离散数学模型分析出Hopf分岔扰动是引起输出电压低频振荡的原因,利用频域法分析其稳定的充要条件,给出Hopf分岔扰动存在性证明,并仿真验证了Hopf分岔扰动的存在。其次,基于理论分析设计模糊推理规则将其与误差反馈控制率结合来提升对Hopf分岔扰动抑制效果。并且,运用频域法理论分析了在Hopf分岔扰动下该控制策略的稳定性及各状态观测误差对干扰的界限。最后,通过仿真分析对比不同工况下此控制策略与传统PI控制策略对Hopf分岔扰动的抑制情况。结果表明,所提出的模糊线性自抗扰控制策略有效地抑制了Hopf分岔扰动,保障了Buck变换器的工作性能。

构网型变流器并网系统在强弱电网下的分岔分析

构网型变流器并网系统在强弱电网下均存在稳定性问题,但这2类稳定性问题之间的联系并不清晰.为此,基于分岔理论揭示了这2类稳定性问题之间的非线性动力学关系和过渡过程的物理图像.首先根据所建模型,对这2类稳定性问题的动力学响应进行分岔分析,得出系统在弱电网下会发生鞍结点分岔,在强电网下会依次发生霍普夫分岔、倍周期分岔并通向混沌.其次基于时间尺度理论进行模型降阶,然后通过小扰动和大扰动分析确定端电压控制是导致强弱电网下系统动力学行为差异的关键因素.之后运用复转矩法进一步揭示了端电压控制会导致系统在强弱电网下分别因阻尼转矩不足和同步转矩不足而失稳.最后通过多机仿真证实了多机系统也存在类似的强电网失稳问题.

不同负载条件下DICM Cuk PFC变换器稳定性分析

重点分析了系统负载变化时,不连续电感电流模式Cuk功率因数校正PFC(power factor correction)变换器稳定性的变化情况。在变换器工作特性的基础上,根据谐波平衡法和Floquet理论分析,研究结果表明:当负载电阻变小时,即系统由轻载到重载变化时,系统发生了工频频率上的倍周期分岔。给出了系统发生倍周期分岔时的电阻,以及在输出电感、输入电压产生改变时和负载电阻共同构成的系统不稳定与稳定的边界区域图,基于输入电感电流-输出电压的相轨图和输出电压的谐波分析谱,更好地观察到系统的动力学行为。最后通过实验验证了理论分析的正确性。

谷值V2控制Boost PFC变换器快时标分岔现象抑制

为抑制Boost PFC变换器中的快时标分岔现象,采用频闪映射的方法对变换器建立数学模型,通过MATLAB/Simulink仿真软件绘制出电感电流的时域波形图和频闪采样图进行分析。施加谷值V2控制对变换器中的快时标分岔现象进行抑制,将传统斜坡补偿控制快时标分岔和谷值V2控制进行比较分析,仿真结果表明:在同等参数条件下谷值V2控制的控制效果较优于斜坡补偿控制,且谷值V2控制具有瞬态响应快、工程应用实现简单等优点。

基于频闪映射的Boost PFC变换器中的间歇性分岔和混沌现象分析

该文推导出了一组频闪映射方程来精确描述峰值电流控制型 Boost PFC 变换器的非线性动力学特性。数值模拟发现了系统电流在输入电压周期内会出现间歇性分岔和混沌现象,并对这种间歇性分岔和混沌的周期性进行了分析。通过对系统占空比的详细研究,发现系统并没有经过倍周期分岔的充分发展到达混沌,而是在倍周期分岔的过程中,发生边界碰撞分岔后以非光滑的方式直接进入混沌的。最后,给出了在输入电压幅值、参考电压和负载变化下系统的稳定域。这些结果对实际电路的设计具有重要的参考价值。

电力电子电路与系统中的复杂行为研究综述

电力电子电路与系统中的复杂行为已经成为近年来电力电子学研究中的一个重要分支,受到了广泛的关注。本文比较系统地介绍了电力电子电路与系统中复杂行为的研究进展,包括这类电路系统的非线性动力学模型的建模方法、分岔产生的机制和通向混沌的道路;讨论了分岔与混沌研究、进行分岔与混沌控制在电力电子电路与系统设计中的实用性和关键性问题;最后,对若干需要研究的问题进行了展望。

电力系统分岔与混沌研究综述

简单介绍了分岔、混沌的基本概念以及电力系统发生的分岔现象,总结了电力系统非线性振荡、次同步谐振、电压失稳和崩溃的机理;电力系统通往混沌的途径以及抑止、延迟电力系统分岔、混沌现象发生以提高电力系统稳定性的方法;混沌理论在电力系统短期负荷预测中的应用。指出了揭示多机电力系统分岔、混沌现象,各种分岔点的快速搜寻方法,电力系统FACTS控制策略,电力系统分岔、混沌控制方法,利用混沌理论对短期负荷进行快速、准确预测是电力系统分岔、混沌研究的发展趋势。

快时标意义下BoostPFC变换器中的分岔与混沌现象分析

导出了电流不连续模式下峰值电流控制型 Boost PFC变换器的离散映射方程。对线周期内的 fast-scale 不稳定现象进行了数值模拟,并对 fast-scale 不稳定区域复杂的非线性行为(例如,倍周期分岔和混沌现象)进行了分析。通过对系统的 Jacobian 矩阵特征值轨迹的分析,定位了周期 1 到周期 2的倍周期分岔点,解析分析与数值结果相吻合。解析分析方法不仅有助于系统电路参数的设计,同时也给系统稳定域边界的预测提供了一种有效的途径。

高阶开关功率变换器中的间歇现象

以四阶电流模式控制单端初级电感变换器(single ended primary inductor converter,SEPIC)为例,研究高阶开关功率变换器中的间歇混沌和间歇分谐波现象。从电路耦合滤波的角度考虑,建立具有耦合干扰信号的SEPIC变换器模型,通过数值仿真和电路仿真观察到了间歇现象,分析不同电路参数对干扰信号强度阈值的影响。并将时间分岔映射为参数分岔,继而以此为基础运用特征值分析方法对变换器的稳定性进行了分析。参数分岔图、特征值轨迹与时间分岔图完全一致,均表明干扰信号的强度和频率决定着间歇现象的类型和间歇周期的大小。

多级并联电流反馈型DC-DC升压变换器中的分岔与混沌

该文利用二维非线性映射的分岔理论分析了多级并联电流反馈型 DC-DC 升压变换器中的分岔与混沌现象,并得出其在相同参数配置下随着级联数增加的变化规律。该文采用离散时间模型法建立了系统在连续电流工作状态下的离散时间映射关系式,并在此基础上进行了分析和计算机仿真。