A fractional-order capacitor (FOC) plays a vital role in fractional-order circuits. However, the FOC with order 1 <; α <; 2 based on existing manufacturing schemes can be only operated in milliwatt power level. Thus, the applications of an FOC in power conversion are limited. To solve the problem, this paper proposes a novel method for realizing a high-power FOC with order 1 <; α <; 2, in which a power converter is applied to emulate the current-voltage characteristic of an ideal FOC, so the rated power of the FOC can be increased greatly and depended on the power converter. The corresponding topology and its control strategy are provided. The available experiments verify the effectiveness of the proposed approach.

In previous studies, researchers used the fractional definition of Caputo to study fractionalorder power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation. The fractional definition is crucial for the application of fractionalorder theory into electric engineering, which directly influences the accuracy of model and operational characteristics of power converter. This paper analyzes fractional-order Buck converter according to the fractional definition of Riemann-Liouville. Firstly, the converter model operating in continuous conduction mode (CCM) is established under Riemann-Liouville fractional definition, and it shows that voltage gain and inductor current are relative with the order, but they are independent of order in the model of Caputo fractional definition. Secondly, the different steady-state characteristics of CCM Buck converter are researched under the models of Caputo and Riemann-Liouville derivative. Finally, the feasible simulations and experiments verify that the model derived by Riemann-Liouville fractional definition is more accurate and suitable for analyzing Buck converter.

The fractional-order capacitor applied in power electronic converters, filters or other circuits has become a hot spot due to benefits, such as high-performance and flexibility. Two typical kinds of fractional-order derivative definitions, Riemann-Liouville (RL) or Caputo derivatives are popularly used to analyze the characteristics of fractional-order capacitor. However, it remains a fundamental challenge to find that when and which fractional-order derivative definition is more suitable in the timedomain analysis of fractional-order capacitor. In this paper, comparative investigations about the transient and steady analysis of a fractional-order capacitor adopting these two definitions are performed. It is determined that difference comes from description of dynamic process. In particular, the difference is especially obvious for the cases of step-up input. Based on the analysis, this paper proposed that RL derivative is a more accurate choice for modeling and analyzing fractional-order capacitor in time domain. Moreover, RL derivative is also more suitable for solving fractional-order circuits with fractional-order capacitor. The results from simulations and experiments verify the conclusion.

Cordless kitchen appliances powered by wireless power transfer (WPT) technology can operate without the clutter of cords, making them safer and easier to clean. In order to allow cordless kitchen appliances to be placed more freely, this article proposed a parity-time (PT) symmetric WPT system with stable output power in the whole coupling range. Here, a new implementation of a PT-symmetric circuit using a combination of self-oscillating methods and pulsewidth modulation (SO-PWM) is presented. The self-oscillating mode is activated in the strong coupling region, which guarantees a constant output power and constant transfer efficiency against the coupling coefficient variation. In the weak coupling region, the PWM mode with a fixed frequency and a variable duty cycle is adopted, and a control strategy based on primary-side-only parameters is presented to obtain stable power transmission. Besides, a corresponding coupling-region detection method based on the reflected resistance is proposed to ensure smooth switching between SO mode and PWM mode. The advantage is that the stable output power can be maintained in the whole coupling region without any extra dc–dc converter and dual-side communication requirements, while maintaining the same transfer efficiency as the standard PT-symmetric WPT system. A 500-W experimental prototype is built to verify the theoretical analysis. The results show that with a transfer efficiency of over 91.6%, the misalignment tolerance can be increased by 172%.

Two kinds of fractional-order autonomous circuits are constructed by using fractional-order capacitor and fractional-order inductor respectively. The orders of the adopted fractional-order elements must be greater than one. The corresponding circuit simulations were developed and verified the proposed fractional-order autonomous circuits.