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| 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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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.
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Received: 29 October 2021
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2023, Vol. 38 
