电工技术学报  2023, Vol. 38 Issue (6): 1553-1563    DOI: 10.19595/j.cnki.1000-6753.tces.211722
电工理论 |
基于激活函数的LCC-S型无线电能传输系统建模和稳定性分析
胡秀芳, 王跃, 吕双庆, 赵德林, 马天录
电力设备电气绝缘国家重点实验室(西安交通大学) 西安 710049
Modeling and Stability Analysis of Wireless Power Transfer System with an LCC-S Compensated Network Based on Activation Function
Hu Xiufang, Wang Yue, Lü Shuangqing, Zhao Delin, Ma Tianlu
State Key Laboratory of Electrical Insulation and Power Equipment Xi'an Jiaotong University Xi'an 710049 China
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摘要 基于电力电子器件的无线电能传输(WPT)系统是一种开关系统,其大信号模型是研究系统运行特性和稳定性的基础。建模的关键是如何描述系统中的非线性、离散开关变量,为解决这一问题,该文提出一种基于S型激活函数的建模方法。S型激活函数是连续、平滑、可微的且在一定值时具有饱和特性,因此可利用陡度因子较大的激活函数来近似开关的切换过程,将WPT系统由离散的开关系统转变为连续系统。该文以LCC-S型WPT系统为研究对象,构建其开环和闭环模式下激活函数模型,利用该模型分析控制器参数和系统参数对瞬态行为和稳定性的影响,并通过仿真和实验进行验证。结果表明,所构建的模型与仿真和实验结果吻合较好。该模型数学表达式结构简单统一,物理意义明确,是一个具有普遍意义的高精度大信号连续模型。
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关键词 无线电能传输系统LCC-S补偿激活函数大信号模型稳定性    
Abstract:Wireless power transfer (WPT) system based on power electronic devices is a switching system, its large-signal model is the basis for studying the operating characteristics and stability of the system. The key to modeling is how to describe the nonlinear and discrete switch variables in the system. In this paper, a modeling method based on sigmoid activation function is proposed to solve this problem. Since the sigmoid activation function is continuous, smooth, differentiable, and saturated at a certain value. Therefore, a sigmoid activation function with a large steepness factor is used to approximate the switching process of the switch, the WPT system is transformed from a discrete switching system to a continuous system. An LCC-S compensated WPT system is selected as an example, and its sigmoid function model in open-loop and closed-loop mode is constructed. However, in closed-loop control mode, the time delay in digital control system is often ignored. Delay link makes WPT system more complicated. For systems without time delay, a certain mapping relationship can be established between input and output. But the existence of time delay may disturb this specific relationship. For the same sampled signal, the time delay in digital control system may lead to the instability of WPT system. The performance of WPT system will inevitably be affected or even deteriorated. Therefore, it is necessary to analyze the stability considering the influence of time delay.
In order to avoid these problems, approximating the time delay in stability analysis becomes a preferred solution. Time delay can be approximated by first-order lag, Taylor expansion, Pade approximation, etc. Compared with the first-order lag and Taylor series, Pade approximation has better performance because of its rational polynomial form. In addition, Pade approximation can handle a relatively short delay. Because the time delay of digital control system is in the order of microseconds, Pade approximation may be more appropriate. Based on the fifth-order pade equivalent approximate delay link, a closed-loop model is established to reveal the instability in the system. The influence of controller parameters and system parameters on transient behavior and stability are analyzed.
In addition, the simulation and experimental platform of the LCC-S compensated WPT system are built in this paper, and the simulation and experimental results verify the validity of the above-derived model. The large signal model established by activation function does not include discontinuous functions, such as sign function, absolute value function or square wave. The discontinuous function in the differential equation of the system is approximated by the activation function in order to make the discontinuous part continuous. From continuous mode to discontinuous mode, the steady and transient processes of the activation function model are consistent with the simulation results of simulation and the experimental results. The results show that the activation function model can accurately describe the transient characteristics of the system. The generalized state-space averaging (GSSA) and extended describing function (EDF) models which are commonly used in WPT systems are compared with model established by activation function, the results show that the model established by activation function model has higher accuracy.
When the system enters into an unstable state, low-frequency oscillation occurs. At this time, the amplitude of voltage and current in the system increases. This phenomenon will increase the stress of the device, or even damage the device. The activation function model, simulation model and experimental waveform in this section clearly describe the steady-state and dynamic characteristics of LCC-S compensation WPT system.
Key wordsWireless power transfer    LCC-S compensation topology    activation function    large signal model    stability   
收稿日期: 2021-10-29     
PACS: TM724  
通讯作者: 王 跃 男,1972年生,教授,博士生导师,研究方向为无线电能传输技术、双有源全桥DC-DC变换器、模块化多电平换流器、虚拟同步发电机。E-mail:davidwangyue@mail.xjtu.edu.cn   
作者简介: 胡秀芳 女,1986年生,博士研究生,研究方向为无线电能传输系统建模和控制。E-mail:huxiufang029@stu.xjtu.edu.cn
引用本文:   
胡秀芳, 王跃, 吕双庆, 赵德林, 马天录. 基于激活函数的LCC-S型无线电能传输系统建模和稳定性分析[J]. 电工技术学报, 2023, 38(6): 1553-1563. Hu Xiufang, Wang Yue, Lü Shuangqing, Zhao Delin, Ma Tianlu. Modeling and Stability Analysis of Wireless Power Transfer System with an LCC-S Compensated Network Based on Activation Function. Transactions of China Electrotechnical Society, 2023, 38(6): 1553-1563.
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