Abstract
In this paper, the fractional-order modeling and analysis of a three-phase voltage source PWM rectifier (VSR) are researched considering the fractional-order characteristics of actual inductors and capacitors. While the Caputo fractional calculus operator is used to describe the fractional-order characteristics of an inductor and a capacitor, the fractional-order model of a three-phase VSR is established in the three-phase static coordinate system. With the coordinate transformation, the fractional-order model is expressed in the two-phase static coordinate system and in the synchronous rotation coordinate system, respectively. Simulation results verify the effectiveness of the established models, and indicate that the fractional-order models can describe the operating characteristics of a three-phase VSR more accurately. Besides, compared with the traditional integer-order three-phase VSRs, the three-phase VSRs which contain the fractional-order inductors and the fractional-order capacitor can present better static and dynamic performance indexes (such as smaller overshoot and shorter regulation time) by appropriately selecting the orders of the inductors and the capacitor.
Highlights
Fractional calculus is developed by extending the order of integer-order calculus from integer to non-integer
We found that the order of inductors affects both the dynamic characteristics and static stability of a three-phase voltage source PWM rectifier (VSR) significantly, while the capacitor order mainly affects the dynamic characteristics
We discovered that the three-phase VSRs which contain the fractional-order inductors and the fractional-order capacitor can present better static and dynamic performance indexes than the traditional integer-order threephase VSRs, by appropriately selecting the orders of the inductors and the capacitor
Summary
Fractional calculus is developed by extending the order of integer-order calculus from integer to non-integer (i.e., fraction, irrational and complex number). The fractional-order modeling of power electronic converters is paid much attention considering the fractional-order characteristics of inductors and capacitors [14]–[26]. The fractional-order model of single-phase voltage source PWM rectifiers was established in the static coordinate system [26], but the inductor was still considered as integer-order model in the simulation. The studies in [14]–[26] indicated that the fractional-order characteristics of inductors and capacitors should be considered in the modeling of the power electronic converters, and the actual operating characteristics can be described more precisely by using fractional-order models. The work of this paper is to address the fractional-order modeling and analysis of a three-phase voltage source PWM rectifier (VSR).
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