The Effect of Fractional Orders on the Transmission Power and Efficiency of Fractional-Order Wireless Power Transmission System

Abstract

To avoid the problems of integer-order magnetic resonant wireless power transmission (WPT) systems, such as low output power and transmission efficiency, high resonant frequency, frequency splitting, and parameter coupling, a novel WPT system based on the fractional-order calculus theory is proposed; the resonant frequency and coupling coefficient can be regulated by the fractional order, so that this system has completely different transmission characteristics from the integer-order WPT system. Therefore, in this paper, the circuit model based on the phasor method of fractional-order WPT system is established, and the output power and transmission efficiency of the system are analyzed. In addition, the comparative analysis of output power and transmission efficiency under different fractional orders are performed to estimate the optimal combination of fractional orders, which is beneficial to produce better characteristics of output power and transmission efficiency and provides a theoretical basis for the design and implementation of an experimental system.

A Fractional-Order Element (FOE)-Based Approach to Wireless Power Transmission for Frequency Reduction and Output Power Quality Improvement

“…A practical FOC is implemented as depicted in Figure 10 based on Ref. [28]. To realize fractional order α = 0.54, the corresponding parameters are: R 1 = 10 kΩ, R 2 = 3.3 kΩ, R 3 = 1.0 kΩ, R 4 = 330 Ω, R 5 = 100 Ω, C 1 = 1.0 µF, C 2 = 470 nF, C 3 = 330 nF, C 4 = 220 nF, C 5 = 100 nF, R p = 22 kΩ, C p = 100 nF.…”

“…In fact, these unique features of FOEs are needed for the applications of WPT. Furthermore, an FOE is mostly constructed into a ladder network consisting of resistors and capacitors (or inductors) [28], which demonstrates that implementation of FOE costs little; however, this still lacks some fundamental studies.…”

Accurate Constant Phase Elements Dedicated for Audio Signal Processing

“…To this end, the modeling of real physical phenomena, where descriptive information is usually available as measured data sequences, by using FO differential equations can be observed in many other research fields. FO wireless power transmission systems are shown in paper [60]. Wideband CPEs need to be utilized while studying chaotic dynamics with the lowest possible order [61] if new FO systems with robust strange attractors are to be discovered [62], or if FO circuit elements should be working in wideband applications such as FO memristors in generators of chaotic waveforms based on Wien bridge oscillator topology [63].…”

Modified method of identification of mutual fractional-order inductance

“…For several years, there has been a rapid growth of interest in fractional differential-integral calculus application in describing fractional-order magneticallycoupled coils systems [4][5][6]. The work [4] describes the concept and properties of such fractional-order coupled inductances.…”

“…In [5], the electromagnetic Maxwell equations of the fractional-order mutual inductance are analyzed. The wireless power transmission system has been modeled as a fractional-order coupled coils system in [6]. The existence of fractional-order coupled coils (fractional-order transformer) implies the need to determine the parameters of the fractional-order elements.…”