Modeling,Analysis And Control Of Fractionalorder PWM Rectifiers And Inverters

The development of fractional-order calculus opens up a new way and provids a new method for the topology construction,modeling,working characteristic analysis,and controller design of control system.Power electronic converters play an increasingly important role in the generation,transmission,and consumption of modern electric energy.Inductors and capacitors are the key components of power electronic converters,which are mainly used for power storage and filtering.Their characteristics will have a decisive influence on the dynamic and static performance of power electronic converters.The research of traditional power electronic converters are all based on integer-order inductors and integer-order capacitors.However,in recent years,more and more research findings have shown that inductors and capacitors are fractional-order in nature.At the same time,scholars have proposed the design and manufacturing methods of fractional-order inductors and fractional-order capacitors with a specified order.The fractional-order gradation of inductors and capacitors will lead reforms to power electronic converters in terms of topological structure,mathematical modeling,working characteristics analysis,and controller design,forming a new development direction.The research on fractional-order power electronic converters is mainly focused on DC/DC converters at present,while the research on AC/DC converters and DC/AC converters involving AC is still in its infancy,and there are still many theoretical and application problems to be solved.In this context,fractional-order inductors and fractional-order capacitors are introduced into traditional voltage source PWM rectifiers(VSRs)and voltage source PWM inverters(VSIs)to construct the main circuits of fractional-order VSRs(FOVSRs)and fractional order VSIs(FOVSIs),and their modeling,analysis,and control problems are further studied.Firstly,the modeling,analysis,and control of a single-phase FOVSR are studied.With the help of the Caputo-type fractional calculus,the switching function model of a single-phase FOVSR is established,and the rotation coordinate transformation of the integer-order AC system is extended to the fractional-order AC system.The synchronous rotation coordinate system(dq coordinate system)model of a single-phase FOVSR is established by constructing dummy variables.On this basis,the phasor method of integer-order system is extended to analyze the sinusoidal steady-state relationship of the AC side of FOVSRs,and the four-quadrant operation vector diagrams of FOVSRs are summarized.Besides,the expressions of the secondary ripple component of the instantaneous power and the DC voltage are derived,and the high-frequency pulsation of the AC side and the DC side caused by PWM pulse changes with the order of inductors and capacitors have been analyzed,respectively.In order to control the stable operation of a single-phase FOVSR,the transient current PI~?controller and the double closed-loop feedforward decoupling PI~?controller in the dq coordinate system are proposed,and the differential evolution algorithm is introduced to find the best parameters of the fractional-order controllers.The correctness of the theoretical derivation and the effectiveness of the controller design are verified by digital simulation.Subsequently,the modeling,analysis,and control of a three-phase FOVSR are conducted.According to the proposed main circuit of a three-phase FOVSR,the switching function model of a three-phase FOVSR in three-phase static coordinate system(abc coordinate system)is established.On this basis,the coordinate transformation from the abc coordinate system to the two-phase static coordinate system(DQ coordinate system)and from the DQ coordinate system to the dq coordinate system of the three-phase fractional-order AC system are realized,and the DQ coordinate system model and the dq coordinate system model of a three-phase FOVSR are established for the first time.Besides,In order to realize independent regulation of active power and reactive power,a double closed loop feedforward decoupling PI~?control method for a three-phase FOVSR in the dq coordinate system is proposed.The effectiveness of the double closed loop feedforward decoupling PI~?control is verified by digital simulation.Then,the modeling,analysis,and control of a single-phase FOVSI are performed.For a single-phase FOVSI with a fractional-order LCL(FOLCL)filter in the AC side,the model in the static coordinate system and in the dq coordinate system are established successively.At the same time,the frequency characteristics of an FOLCL filter are studied systematically.The conditions of resonance of an FOLCL filter,and the calculation formula of the resonance frequency and the asymptote slope of logarithmic amplitude frequency characteristics are derived.The change law of phase crossover frequency and gain crossover frequency is analyzed.Besides,Five important working properties of FOLCL filters are found,for example,the"resonance property"reveals that the necessary and sufficient condition for the existence of resonance in an FOLCL filter is that the sum of the order of fractional-order inductors and fractional-order capacitor is equal to 2,which provides a theoretical basis for FOLCL filters to avoid resonance effectively.For the single-phase FOVSI with and without resonant peak,PI~?control with capacitive current feedback and without capacitive current feedback is proposed,respectively,and the latter method can simplify the structure of the controller.In order to eliminate the influence of the background harmonic in the grid connected FOVSIs,the fractional power grid voltage feedforward auxiliary control strategy is also deduced.The correctness of the theoretical derivation and the effectiveness of the controller design are verified by digital simulation.Finally,the modeling,analysis,and control of a three-phase FOVSI are studied.The abc coordinate system model,the dq coordinate system model and the dq coordinate system model of a three-phase FOVSI are established successively.On this basis,the PI~?controller in the DQ coordinate system and in the dq coordinate system of a three-phase FOVSI are proposed,respectively.The former control structure is relatively simple,but there are steady-state errors in active and reactive power;the latter control structure is relatively complex,but the active and reactive power can be directly controlled,and the steady state error of the active and reactive power can be eliminated.In addition,through digital simulation,it is found that PI~?control is superior to PI control in tracking accuracy of given value,harmonic proportion,active and reactive power regulation.In general,the circuit,modeling,analysis,and control of VSRs and VSIs are extended from integer-order to fractional-order,which expands the concept and scope of VSRs and VSIs,and forms a complete fractional-order AC/DC and DC/AC power electronic converter architecture of"fractional-order object+fractional-order control".In particular,the rotation coordinate transformation is successfully extended from the integer-order AC system to the fractional-order AC system,which opens up a new method for modeling fractional-order systems in the field of electrical engineering.Compared with traditional VSRs and VSIs,due to the introduction of fractional-order,FOVSRs and FOVSIs present more flexible and diverse operating characteristics,and FOVSRs and FOVSIs with better performance can be designed by properly select the orders of the inductors and the capacitors.