Engineering Mathematics and Physics Dept, Faculty of Engineering, Cairo University, Giza, Egypt; Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt.
Electronics and Communications Department, Cairo University, Giza, Egypt.
ISA Trans. 2018 Nov;82:184-199. doi: 10.1016/j.isatra.2017.06.024. Epub 2017 Jul 11.
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach.
由于商用感应器存在不理想性，因此需要更好的模型来准确描述其动态响应，这使得 Buck、Boost 和 Buck-Boost DC-DC 转换器的分数阶模型在本文中得以呈现。本文对转换器的两种最常见工作模式：连续导通模式（CCM）和不连续导通模式（DCM）进行了详细分析。针对感应器电流、电压增益、平均电流、导通时间和功率效率推导出了时域的闭式表达式，其中发现感应器的分数阶效应非常明显。例如，在稳态下，感应器峰值电流随感应器阶数的降低而增加。使用先进设计系统（ADS）电路仿真来验证推导的公式，其中使用 Valsa 常数相位元件（CPE）逼近和广义阻抗转换器（GIC）来模拟分数阶感应器。对于三种不同分数阶的 DC-DC 转换器拓扑结构，介绍了不同的仿真结果，与理论公式吻合良好。与最近发表的文献进行了全面比较，展示了每种方法的优缺点。
