首先基于分数阶微积分理论分析讨论分抗元件的基本特性,并在Matlab/Simscape平台搭建分抗元件的器件级仿真模块,以实现分数阶逆变系统的器件级仿真;其次建立三相并网逆变器的分数阶高低频数学模型,推导分数阶电流内环的解耦控制结构,并引入分数阶PIλ控制器建立分数阶光伏并网双闭环控制系统。仿真结果表明：所建分抗元件仿真模块能在所选频率段准确模拟分抗元件外特性,分数阶光伏三相逆变器拥有更好的动静态特性,分数阶双闭环控制效果明显优于整数阶双闭环控制。
Abstract
This paper firstly analyzes and discusses the basic characteristics of the fractional reactance element, and builds a simulation module of the fractional reactance element on the Matlab/Simscape platform to realize the device-level simulation of the fractional-order photovoltaic inverter system. Secondly, the fractional-order high-frequency mathematical model of the three-phase photovoltaic grid-connected inverter is established, the decoupling control structure of the fractional-order current inner loop is deduced, and a fractional-order controller is introduced to establish a fractional-order photovoltaic grid-connected double closed-loop control system. The simulation results show that the built fractional reactance element simulation module can accurately simulate the external characteristics of the fractional reactance element in the selected frequency range, the fractional-order photovoltaic three-phase inverter has better dynamic and static characteristics, and the fractional-order photovoltaic double closed-loop control effect is obviously better than integer-order double closed-loop control.
关键词
逆变器 /
光伏并网 /
分数阶微积分 /
PIλ /
解耦控制
Key words
electric inverters /
PV grid connection /
fractional calculus /
PIλ /
decoupling control
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参考文献
[1] FREEBORN T J, MAUNDY B, ELWAKIL A S.Measurement of supercapacitor fractional-order model parameters from voltage-excited step response[J]. IEEE journal on emerging and selected topics in circuits and systems, 2013, 3(3): 367-376.
[2] JONSCHER A K.Dielectric relaxation in solids[J]. Journal of physics D: applied physics, 1999, 32(14): R57.
[3] 孙会明, 陈薇, 孙龙杰, 等. Buck变换器的分数阶仿真模型与混沌分析[J]. 现代电子技术, 2014, 37(24): 154-159, 162.
SUN H M,CHEN W,SUN L J,et al.Fractional order simulation model and chaos analysis of Buck converter[J]. Modern electronics technique, 2014, 37(24): 154-159,162.
[4] WEI Z H, ZHANG B, JIANG Y W.Analysis and modeling of fractional-order buck converter based on Riemann-Liouville derivative[J]. IEEE access, 2019, 7: 162768-162777.
[5] 王发强, 马西奎. 电感电流连续模式下Boost变换器的分数阶建模与仿真分析[J]. 物理学报, 2011, 60(7): 89-96.
WANG F Q,MA X K.Fractional order modeling and simulation analysis of Boost converter in continuous conduction mode operation[J]. Acta physica sinica, 2011, 60(7): 89-96.
[6] 柴秀慧, 曹晗, 张波, 等. Boost变换器全分数阶化系统分析与控制性能研究[J]. 电源学报, 2019, 17(6): 27-33.
CHAI X H, CAO H, ZHANG B, et al.Research on analysis and control performance of full fractional-order Boost converter system[J]. Journal of power supply, 2019, 17(6): 27-33.
[7] 王发强, 马西奎. 基于分数阶微积分的电感电流断续模式下Boost变换器的建模与分析[J]. 中国科学: 技术科学, 2013, 43(4): 368-374.
WANG F Q, MA X K.Modeling and analysis of Boost converter in discontinuous mode of inductor current based on fractional calculus[J]. Scientia sinica:technologica, 2013, 43(4): 368-374.
[8] 胡旭旭, 范秋华. Buck-Boost变换器断续模式下的分数阶建模与分析[J]. 现代电子技术, 2020, 43(24): 126-130, 134.
HU X X, FAN Q H.Fractional-order modeling and analysis of Buck-Boost converter in disdiscontinuous conduction mode[J]. Modern electronics technique, 2020, 43(24): 126-130, 134.
[9] WU C J, SI G Q, ZHANG Y B, et al.The fractional-order state-space averaging modeling of the Buck-Boost DC/DC converter in discontinuous conduction mode and the performance analysis[J]. Nonlinear dynamics, 2015, 79(1): 689-703.
[10] ZHU P F, WEI Y F, ZHENG Z, et al.Fractional modelling and simulation for single-phase PWM rectifier[J]. The journal of engineering,2019, 2019(16): 1675-1678.
[11] XU J H, LI X C, MENG X R, et al.Modeling and analysis of a single-phase fractional-order voltage source pulse width modulation rectifier[J]. Journal of power sources, 2020, 479: 228821.
[12] XU J H, LI X C, LIU H, et al.Fractional-order modeling and analysis of a three-phase voltage source PWM rectifier[J]. IEEE access, 2020, 8: 13507-13515.
[13] 党选举, 李晶晶, 姜辉, 等. 基于分数阶微分补偿算法的光伏系统MPPT研究[J]. 太阳能学报, 2015, 36(9): 2117-2123.
DANG X J, LI J J, JIANG H, et al.Research on MPPT of photovoltaic system based on fractional differential compensation algorithm[J]. Acta energiae solaris sinica, 2015, 36(9): 2117-2123.
[14] 宋平岗, 杨声弟. 光伏阵列多峰特性情况下的最大功率点跟踪策略[J]. 太阳能学报, 2020, 41(10): 144-150.
SONG P G, YANG S D.Maximum power point tracking strategy of PV array with multi-peak characteristics[J]. Acta energiae solaris sinica, 2020, 41(10): 144-150.
[15] MONJE C A, CHEN Y Q, VINAGRE B M, et al.Fractional-order systems and controls: fundamentals and applications[M]. Berlin: Springer Science & Business Media, 2010.
[16] DAS S.Functional fractional calculus[M]. Berlin: Springer Science & Business Media, 2011.
[17] 张兴. PWM整流器及其控制[M]. 北京: 机械工业出版社, 2012: 99-106.
ZHANG X.PWM rectifier and its control[M]. Beijing:China Machine Press, 2012: 99-106.
[18] 薛定宇. 分数阶微积分学与分数阶控制[M]. 北京:科学出版社, 2018: 260-268.
XUE D.Fractional calculus and fractional-order control[M]. Beijing: Science Press, 2018: 260-268.
基金
国家自然科学基金（51267001）; 广西自然科学基金（2014GXNSFAA118338）; 广西科学研究与技术开发计划（14122006-29）; 南宁市科学研究与技术开发计划（20165186）
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