摘要
谐振变换器能利用自身的谐振过程实现软开关,从而提高开关频率,使电力电子设备高频化,符合现代电力电子技术的发展趋势,目前谐振变换器在静电除尘、医疗设备等高压应用场合的使用越来越广泛。但谐振变换器通常是一个强非线性系统,其建模、电路分析和设计过程十分繁琐,因此目前对于谐振变换器的精确数学模型、快速仿真技术和优化技术的研究需求越来越迫切。针对高压应用场合谐振变换器的拓扑特点,本文研究了具有电容输出滤波器的并联谐振变换器和LCC谐振变换器的建模、优化和控制技术,为其在高压场合的应用提供了研究基础。
本文将图论理论引入到谐振变换器的谐振模态分析中。在获取了并联谐振变换器和LCC谐振变换器的所有工作通路路径的基础上,根据这两种谐振变换器的电路拓扑特点和工作原理,筛选出有效通路路径,并且根据有效通路得到这两种谐振变换器的全部谐振模态。研究过程表明,图论分析形象直观,简单易行,计算方便,是一种可用于多谐振模态下谐振变换器的分析方法。
对并联谐振变换器和LCC谐振变换器的时域建模进行了深入研究。在时域模型的基础上进行了电路特性分析,找出了谐振元件参数选择与电路特性之间的关联,推导出了能满足设计要求的谐振元件参数的计算表达式,总结出了谐振变换器时域建模与分析的一般步骤。
用状态平面分析法推导了LCC谐振变换器谐振槽电容电压和电感电流的稳态轨迹方程,在此基础上绘制了状态轨迹图,并用平面几何方法研究了这种拓扑结构的谐振电路物理量之间的几何关系,稳态轨迹分析使时域模型中状态变量的动态变化更直观,物理意义更明确。在稳态轨迹基础上,提出一种简单、有效的轨迹控制方法,该方法能使LCC谐振变换器在工作状态切换时在很短的时间内达到稳态,实现无振荡转换。
在傅立叶级数分析的基础上,运用动态相量法建立了LCC谐振变换器的大信号模型和稳态模型。大信号模型避免了建立在“准稳态”假设基础上的电路模型不能仿真变化迅速暂态过程的缺陷,通过与时域模型的仿真结果对比,验证了大信号模型的精确性和仿真快速性。然后,在大信号模型的基础上,考虑占空比和开关角频率的扰动建立了小信号模型,并用它分析了系统性能。最后,通过与基于平衡点的线性化模型仿真结果对比验证了小信号模型的准确性。动态相量建模实现了变化迅速暂态过程的仿真,极大加快了仿真速度,并且有效实现了谐振变换器的动态特性分析。
为了优化LCC谐振变换器的系统性能,对多目标优化遗传算法的应用进行了具体研究。首先,在动态相量稳态模型的基础上得到了反映其系统性能的数学表达式。然后,提出用一种基于Pareto的多目标优化遗传算法对谐振变换器的系统性能进行优化计算。该算法用包含密度信息的细粒度赋值策略通过最小化目标函数获得了一组均匀分布的最优解集,由这组最优解集可推导出相应的谐振电路元件参数,从而指导电路设计。多目标优化遗传算法在不依靠决策偏好信息的条件下对研究对象进行多目标优化,避免了人为因素对最优设计方案造成的偏差,具有很好的实际应用价值。最后,仿真和实验结果验证了这种多目标优化设计方法的正确性。
Soft-switching of resonant converter can be realized by its own resonant process, so as toimprove the switching frequency, make power and electronic equipment of high frequency bein line with the development trend of power and electronic technology. At present theapplication of resonant converters has become more and more widely, such as static dustremoval medical devices and so on. However, resonant converter is popularly a strongnonlinear system, its modeling, circuit analysis and design are very difficult, so the study ofresonant converter is more and more urgent in terms of the accurate mathematical model fastsimulation technology and optimization technique. According to the topology characteristicsof resonant converters in high-voltage applications, the modeling optimization method andcontrol method of parallel resonant converter&LCC resonant converter with capacitiveoutput filter have been studied in this paper, and the research basis is provided for itsapplication in high-voltage applications.
The graph theory is applied to multiple resonant modes analysis of resonant converters.Firstly all operating paths of parallel resonant converter&LCC resonant converter withcapacitive output filter are found by graph theory. Then the valid paths are derived in terms ofcircuit topology characteristics and operating law of the resonant converters. Finally the validresonant modes are obtained by these valid paths. The analysis method which is based ongraphic theory is verified by the simulation and experimental process. This proposed methodcan be used for analysis of resonant states of resonant converters easily and intuitively.
In this paper, the time-domain mathematic models of parallel resonant converter&LCCresonant converter with capacitive output filter are studied in detail. Based on thetime-domain mathematic models, the circuit characteristics are studied, the relation betweenthe resonant tank component value choices and the circuit characteristics is obtained, theanalytic expressions are deduced to meet the requirements of circuit design, and the generalsteps of time-domain modeling and analysis is summarized.
The state track diagram of LCC resonant converter is drew, the trajectory equations ofthe inductance current&the capacitance voltage are derived in this paper, the circuit topologystructure of LCC resonant converter is simply studied by a geometric analysis method, so thedynamic variation process of the state variables is more intuitive, more definite physicalmeaning. Based on the steady state trajectory, a simple and effective trajectory control methodis given, the trajectory control system has excellent transient performance and can achieve thenew steady state in minimum time by this method.
Based on Fourier series, a large-signal model and a steady mathematic model of the LCCresonant circuit are established using dynamic phasor. This modeling method of large-signalmodel avoids the limitation that the circuit model which is established by the quasi-stationaryassumption can’t simulate the vertiginous transient process, the excellent tracking behaviorand fast simulation speed of the large-signal model are verified by comparison withtime-domain model. Then, based on the large-signal model, a small-signal model is set upconsidering perturbation of the duty cycle and switching angular frequency, the systemperformance can be analyzed by this small-signal model. Finally, the small-signal model isverified by comparison with the perturbation simulation results of the linear model. Dynamicphasor modeling can simulate the vertiginous transient process, speed up the simulation speedgreatly, and realize the dynamic characteristics analysis of the resonant converters.
In order to improve the system characteristics of LCC resonant converter with capacitiveoutput filter, the applications of multi-objective genetic algorithm are studied in detail. Firstly,the calculation expressions of the circuit characteristics are obtained based on the steadymathematic model. Then, a Pareto multi-objective optimization with genetic algorithm isapplied to improve the system characteristics of LCC resonant converter. With fine-grainedfitness assignment strategy and density estimation, the algorithm can achieve massive andwell-distributed optimal solutions by the minimization of objective functions, these optimalsolutions can be used to direct design of the circuit. In the condition of not relying on decisionpreference information, multi-objective optimization of the research objects can be completedby multi-objective genetic algorithm, so design deviation of the optimal scheme caused byman-made factors can be avoided. This proposed multi-objective genetic algorithm has goodapplicable value. Finally, it is verified by the results of simulation and experiment.
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