感应耦合电能传输系统稳定域的分析

Analysis on the regions of stability for inductive coupled power transfer systems

感应耦合电能传输(inductive coupled power transfer,ICPT)技术是目前应用最为广泛的无线电能传输技术.应用软开关技术能提高ICPT系统的效率,但同时也带来了多软开关工作点(频率分叉)问题,使系统呈现复杂的动态特性.通过求解极限环的稳定域(region of stability,RoS)可以对其背后的原理进行很好的解释.本文以串联谐振型ICPT系统为例,首先对其建立了分段线性模型与碰撞映射模型,并利用ICPT系统的对称特性将碰撞映射模型进行了简化.通过理论分析,推导出基于二次型李雅普诺夫函数的稳定性判据.设计算法,以稳定性判据为约束条件,RoS体积为目标函数,通过遗传算法实现了RoS的求解.最后通过实例对此方法进行了验证.相比于现有方法,本方法求得的RoS体积更大,从而更好地解释了软开关ICPT系统的动态特性.本文所提出的方法也可用于求解其他分段线性系统的极限环RoS,为这类系统的研究与设计提供了一定的参考.

Inductive coupled power transfer(ICPT) is the most widely used technology for wireless power transferring.To improve the efficiency, soft-switching technology is usually applied to ICPT systems. However, soft switching also brings the problem of multiple soft-switching frequency, which makes the behavior of ICPT systems complex. Such behavior could be well explained by the regions of stability(RoS). With series-series ICPT systems as an example, this paper proposed an improved algorithm for computing the RoS of ICPT systems. First, both the piecewise linear model and impact map model are constructed. Taking advantage of ICPT systems' symmetry, the impact model is simplified. Then the stability criteria based on quadratic Lyapunov function are derived. With stability criteria as constraints and the size of RoS as an object, the RoS is obtained by genetic algorithm. At last, the proposed method is verified by an example system.The resulting RoS of the proposed method is much larger than the results of existing methods, making the characteristics of soft-switching ICPT systems clearer. The proposed method can also be used to compute the RoS of limit cycles for other piecewise linear systems, making it useful when studying and designing such systems.