摘要
实际存在的电感和电容事实上是分数阶元件。对于含有分数阶元件的电路,利用整数阶的方法显然无法获得准确的电路特性,且由于分数阶算子具有记忆和遗传效应,使得分数阶电路的分析繁琐复杂。因此,基于分数微积分理论,将整数阶的相量法推广应用于分数阶电路的分析中。给出了分数阶电感和分数阶电容的相量形式,分析了它们的阻抗及功率特性,研究了分数阶RLC串并联电路以及复杂分数阶电路的正弦稳态特性,探讨了分数阶元件的阶次对电路有功功率和无功功率的影响,仿真计算验证了相量法在分数阶电路中应用的正确性。
Due to the fact that the real inductor and the real capacitor are the fractional-order components in fact, the integer-order method cannot analyze the characteristics of the fractional-order circuits accurately, and the analysis of the fractional-order circuits becomes complicated because of memory and hereditary properties of the fractional-order operator. So, based on the fractional calculus theory, the phasor method is generalized to the analysis of the fractionalorder circuits. Phasors of the fractional-order inductor and the fractional-order capacitor are given. The characteristics of the impedance and power are analyzed. The sinusoidal steady states of the fractional-order RLC circuits and the complex fractional-order circuit are studied. The influences of orders of the fractional-order components on the active power and the reactive power are analyzed. The simulation results verify the correctness of the phasor method.
出处
《电源学报》
CSCD
2017年第4期34-40,共7页
Journal of Power Supply
基金
国家自然科学基金重点资助项目(51437005)~~
关键词
相量分析
数值仿真
分数阶电感
分数阶电容
正弦稳态特性
phasor analysis
numerical simulation
the fractional-order inductor
fractional-order capacitor
characteristics of sinusoidal steady state
