针对电容电感都为分数阶这一事实,利用分数阶微积分R-L定义和状态空间平均法,对工作在电感电流连续模式（CCM）下的分数阶Flyback变换器进行建模与分析。推导CCM分数阶Flyback变换器的静态工作点和小信号传递函数以及变换器工作在CCM模式下的条件。其次,讨论Caputo模型与R-L导数模型的区别,得出在R-L分数阶定义下直流静态工作点不仅与占空比相关,而且还与电感和电容的阶数以及负载有关。最后,在PSIM中搭建R-L分数阶CCM Flyback变换器电路模型,得到不同分数阶电感电容阶数下分数阶Flyback变换器输出电压和电感电流的仿真波形,通过仿真结果与理论计算结果对比,验证所建模型的正确性,得出分数阶电感电容的阶数会影响闭环控制器的设计和分数阶模型能更加精确地描述Flyback变换器的工作特性。
Abstract
In view of the fact that capacitors and inductors are fractional order, fractional-order Flyback converters operating in current continuous mode (CCM) are modeled and analyzed by using fractional-order calculus R-L definition and state-space averaging method. The mean state model, boost ratio, DC static equilibrium point, inductor cur-rent ripple and the condition of CCM Flyback converter working in CCM mode are derived. Secondly, the difference between Caputo model and R-L derivative model is discussed. It is concluded that the DC static operating point and boost ratio under R-L fractional order definition are not only related to duty ratio, but also related to the order of inductance and capacitance and load. Finally, the circuit model of R-L fractional-order CCM Flyback converter was built in PSIM, and the simulation waveforms of the output voltage and inductance current of fractional-order Flyback converter were made under different fractional-order inductance and capacitance orders. By comparing the simulation results with the theoretical calculation results, the correctness of the model was verified. It is concluded that the fractional-order Flyback converter model derived from R-L definition can more accurately describe the operating characteristics of CCM fractional-order flyback converter.
关键词
DC-DC变换器 /
电力电子 /
仿真平台 /
R-L定义 /
分数阶建模
Key words
DC-DC converters /
power electronics /
simulation platform /
R-L definition /
fractional-order modeling
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基金
国家自然科学基金（12072205）; 河北省省级科技计划（21341801D）; 国网河北省电力有限公司科技项目（kj2022-015）
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