三相并网逆变器的分数阶PCI控制技术

Fractional-order PCI Control Technology for Three-phase Grid-connected Inverter

针对比例谐振和比例复数积分控制器都存在谐振项带宽偏低的问题,提出一种更具普遍形式的分数阶比例复数积分控制器。首先,论证比例积分、比例谐振和比例复数积分等控制器均是分数阶比例复数积分的特殊形式,给出分数阶比例复数积分的谐振项带宽与阶次的关系,并合理选取控制器阶次;其次,构建三相并网逆变器在分数阶比例复数积分控制下的数学模型,证明系统的输出不存在稳态误差,并利用开环截止频率和主导极点确定相关参数;最后,进行对比仿真测试,结果验证了所提控制算法的有效性和优越性。

Aimed at the problem that the resonator bandwidth is lower which exists in both the proportional resonance(PR)and proportional complex integral(PCI)controllers,a kind of more commonly-utilized fractional-order propor⁃tional complex integral(FOPCI)controller is put forward.First,it is proved that the controllers such as proportional in⁃tegral(PI),PR and PCI are all specific forms of the FOPCI controller.The relationship between the resonator band⁃widths and orders of the FOPCI controller is given,and the order of the controller is properly selected.Then,the mathe⁃matical model of a three-phase grid-connected inverter controlled by the FOPCI controller is built,and it is proved that there is no steady-state error in the system output.In addition,the related parameters are determined by means of the open-loop cut-off frequency and dominant pole.Finally,contrast simulations are carried out,and results show the valid⁃ity and superiority of the proposed control method.