A fractional-order integral sliding mode auto-disturbance rejection control method for Vienna rectifier

Abstract

The present invention discloses a Vienna rectifier fractional-order integral sliding mode self-disturbance rejection control method. The method uses a power loop control based on a fractional-order integral sliding mode to reduce the waveform distortion of the three-phase input current on the grid side and ensure that it can operate at a high power factor. In addition, the method applies the self-disturbance rejection control strategy to the control of the voltage outer loop to achieve high-precision voltage tracking. Finally, simulation verifies that the Vienna rectifier control method provided by the present invention improves the dynamic and static performance and anti-disturbance capability of the Vienna rectifier, and can improve the stability of the bus voltage.

Description

Technical Field

[0001] The invention belongs to the field of aviation secondary energy control, and in particular relates to a Vienna rectifier fractional-order integral sliding mode auto-disturbance rejection control method. Background Art

[0002] The constant speed and constant frequency AC power supply system is the earliest AC power supply system used in aircraft. It mainly uses a variable speed gearbox device to convert the variable engine shaft speed into a constant speed output, thereby driving the AC generator to generate constant frequency AC power. Due to the complex structure of the variable speed gearbox device, the weight of the engine is increased, which is not conducive to maintenance and control, and the constant speed and constant frequency power supply is difficult to achieve starting / power generation integration. Therefore, the variable frequency constant speed AC power supply that cancels the constant speed gearbox device has gradually attracted attention. After the further development of the aircraft power supply system, the variable frequency AC power supply system with a simpler structure, higher safety and higher energy conversion efficiency has gradually become the mainstream power supply system. With the development of more electric aircraft and electric propulsion aircraft plans, the proportion of the power system is increasing. Electricity is not only used for secondary systems, but also as a propulsion energy source, resulting in a continuous increase in power demand. Therefore, the high-voltage DC power supply system has gradually attracted attention. For the aircraft primary power supply (AC generator) based on the high-voltage DC power supply system, it is usually necessary to rectify first to achieve AC-DC conversion. In order to ensure the safe and efficient operation of the aviation rectifier system, the rectifier is required to have a high density and energy conversion efficiency, and to reduce the impact on the input current.

[0003] The PWM-controlled rectifier has good input-output characteristics, can realize closed-loop control of the output voltage, has less harmonic components in the grid-side current, and significantly improves the power density compared to passive rectifiers. Among them, the three-phase Vienna rectifier is very suitable as a rectifier device for aircraft power systems because of its advantages such as small voltage stress on power devices, small input current harmonics, and high structural reliability. Summary of the invention

[0004] Purpose of the invention: In view of the above background technology, a Vienna rectifier fractional-order integral sliding mode auto-disturbance rejection control method is proposed, which can improve the stability of the bus voltage and achieve high-precision voltage control.

[0005] Invention content: A Vienna rectifier fractional-order integral sliding mode auto-disturbance rejection control method comprises the following steps:

[0006] A Vienna rectifier fractional-order integral sliding mode auto-disturbance rejection control method comprises the following steps:

[0007] Step 1: Analyze the topological structure of Vienna rectifier, and establish the mathematical model of Vienna rectifier in three-phase stationary coordinate system and two-phase rotating coordinate system in combination with Kirchhoff's voltage and current theorem;

[0008] Step 2: Combine sliding mode with fractional-order control for the power inner loop of Vienna rectifier and design a fractional-order integral sliding mode controller;

[0009] Based on the fractional-order integral sliding surface, active power and reactive power are selected as inner loop control variables, and the established mathematical model is combined with the designed sliding surface to design a fractional-order integral sliding mode control scheme for the power inner loop.

[0010] Step 3: Design linear anti-disturbance control for the voltage outer loop, with the DC side voltage as input and the active power command value as output. Design the tracking differentiator, linear extended state observer and linear state error feedback control law respectively, and then obtain the final control law of the Vienna rectifier to realize the fractional-order integral sliding mode anti-disturbance control of the Vienna rectifier.

[0011] Furthermore, in step 1, the mathematical model of the Vienna rectifier is as follows:

[0012] For the Vienna rectifier, the following assumptions are made:

[0013] (1) All power devices, wires, capacitors, inductors, diodes and other devices are lossless ideal devices;

[0014] (2) The power input voltage is an ideal sine wave, and the input inductor works in a linear state and will not saturate;

[0015] (3) The switching frequency is much greater than the fundamental frequency of the power supply;

[0016] The phase current of the Vienna rectifier can flow in both directions in the branch according to the direction of the current when the power switch tube is turned on; when the switch tube is cut off, the current of the branch is zero, that is, the branch is completely disconnected; that is, each phase bridge arm of the rectifier is divided into three different modes according to the direction of current flow and the switching state; the switch function group is defined as follows:

[0017]

[0018]

[0019]

[0020] Among them, S ap , S an , S ax They are the equivalent switching states of phase A respectively.

[0021] Based on Kirchhoff's voltage and current theorem and combined with the Vienna rectifier topology, the state equation expression in the three-phase stationary coordinate system, i.e., the abc coordinate system, is obtained:

[0022]

[0023] Where X = [i a i b i c V c1 V c2 ] T , E=[e sa e sb e sc 0 0] T , B=diag[1 1 1 0 0], Z=diag[L a L b L c C1 C2]. sa 、e sb 、e sc is the three-phase voltage of the AC power supply; L a , L b , L c is the AC side energy storage filter inductor; V c1 、V c2 are the upper and lower capacitor voltages on the DC side of the Vienna rectifier respectively; L is the three-phase inductance on the AC side; R is the resistance on the AC side; C1 and C2 are the capacitors on the DC side, let C1=C2=C; i a 、i b 、i c is the three-phase current on the AC side;

[0024]

[0025] Among them, R L Output load resistance;

[0026] By performing Clark transformation on equation (4), the Vienna rectifier expression in the two-phase rotating coordinate system, i.e., the αβ coordinate system, is:

[0027]

[0028] Among them, S αp , S βp , S αn , S βn is the switch state in the αβ coordinate system; i α and i β is the grid-side current in the αβ coordinate system; e α and e βis the grid-side voltage in the αβ coordinate system; i R is the output current;

[0029] Written in matrix form:

[0030]

[0031] Among them, Z αβ =diag[LL C1 C2],X αβ =[i α i β V c1 V c2 ] T , B αβ =diag[1 1 0 0],E αβ =[e α e β 0 0],

[0032] Furthermore, the step 2 includes the following specific steps:

[0033] Step 2-1: According to the instantaneous power theory, the instantaneous power expression is:

[0034]

[0035] Among them, P and Q are instantaneous active power and reactive power respectively;

[0036] The voltage on the grid side of the Vienna rectifier is expressed as:

[0037]

[0038] Where, ω is the angular frequency of the AC power supply;

[0039] By taking the derivative of equation (7) and combining equations (6) and (8), the differential expression for instantaneous power is obtained:

[0040]

[0041] Among them, v α 、v β is the vector voltage;

[0042] Transform the DC side equation in equation (6) so that both sides of the DC side voltage equations are added and multiplied by V dc , we get the DC side power equation:

[0043]

[0044]

[0045] Among them, P dc is the DC side power, which is the sum of the load power and the power of the two DC energy storage capacitors; V dc is the DC side voltage of Vienna rectifier;

[0046] Step 2-2: Given the grid-side active power and reactive power of the rectifier are P ref , Q ref , the power tracking error is expressed as:

[0047]

[0048] Where, e represents the error vector;

[0049] The designed fractional-order integral sliding mode function is:

[0050] s=e+cD -u e (13)

[0051] Wherein, c=diag{c1,c2} is the integral constant matrix, c1>0, c2>0; 0<u<1; s is the sliding mode function; D is the linear operator, and u represents the order of fractional differential;

[0052] Select the exponential reaching law:

[0053]

[0054] Among them, ε=diag{ε1, ε2}, ε1>0, ε2>0, k=diag{k1,k2}, k1>0, k2>0;

[0055] The derivative of the sliding surface is:

[0056]

[0057] in,

[0058] The control law expression of the inner loop controller can be obtained from equations (14) and (15):

[0059] V αβ =M -1 [F+cD 1-u e+ks+εsgn(s)] (16)

[0060] Furthermore, the stability of the designed sliding mode control law is analyzed.

[0061] The Lyapunov equation is selected as follows:

[0062]

[0063] The first-order derivative is:

[0064]

[0065] Let s = [s1 s2] T , then according to equations (13), (14) and (18), we can obtain:

[0066]

[0067] Because ε1>0, ε2>0, k1>0, k2>0, s1 has the same sign as ε1sgn(s1)+k1s1, and s2 has the same sign as ε2sgn(s2)+k2s2, that is, the sliding surface function s and the sliding surface derivative ds / dt have opposite signs, indicating that the reachability condition of the sliding surface is satisfied, and s1[ε1sgn(s1)+k1s1]+s2[ε2sgn(s2)+k2s2]>0. Therefore, the designed controller can meet the stability requirements.

[0068] Furthermore, the design of linear active disturbance rejection control for the voltage outer loop in step 3 includes the following specific steps:

[0069] Consider the rectifier operating at unity factor, i.e. Q ref =Q=0; given DC output voltage is V ref ,When the switching loss of the power devices in the circuit and the equivalent impedance loss are ignored, the power consumed on the DC side is equal to the input power on the AC side. The transformation of equation (11) is:

[0070]

[0071] Let y = V ref 2 、f=-4V ref 2 / CR L , b=4 / C, u=P, then equation (20) can be transformed into:

[0072]

[0073] Furthermore, the design of the tracking differentiator in step 3 includes the following specific steps:

[0074] The desired output voltage of the Vienna rectifier is V ref , design the tracking differentiator to make a smooth transition of the control signal to reduce the initial error. For the voltage outer loop, the tracking differentiator is set as:

[0075]

[0076] Among them, r is the adjustable speed factor, which is mainly used to adjust the rising speed during the transition process; v1 is the arranged transition process; v2 is the generalized derivative of v1; V dc is the DC side voltage of Vienna rectifier.

[0077] Furthermore, the design of the linear extended state observer in step 3 includes the following specific steps: taking the controller input V dc And output u=P ref To estimate and track the various state quantities and total disturbance of the system, we have:

[0078]

[0079] Among them, z1 is the estimate of the DC side voltage; z2 is the estimate of the internal and external disturbances of the rectifier; β1 is an adjustable parameter, and β2 is usually adjusted by expanding the bandwidth of the state observer.

[0080] Furthermore, the design of the linear state error feedback control law in step 3 includes the following specific steps:

[0081] The error of DC voltage is used as the feedback control quantity, and the disturbance estimation is compensated in real time. The design of linear state error feedback law is as follows:

[0082]

[0083] Among them, z1 is the estimate of the DC side voltage; z1 is the estimate of the internal and external disturbances of the rectifier; v1 is the lonely process of the arrangement; k s It is an adjustable parameter.

[0084] Beneficial effects: Compared with the existing known methods, the advantages of the present invention are as follows: 1) The voltage outer loop control scheme does not rely on the accurate model of the Vienna rectifier, reducing the error caused by modeling deviation; 2) When facing external disturbances such as internal disturbances of Vienna rectifier parameters, changes in load characteristics and changes in environmental conditions, the system has excellent anti-disturbance capabilities; 3) Reduce the three-phase current waveform distortion and high power factor on the AC side of the Vienna rectifier to ensure control quality; 4) Have a faster dynamic response speed during the voltage building process. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 A topological structure diagram of a Vienna rectifier in an embodiment of the present invention;

[0086] Figure 2 This is a schematic diagram of Vienna rectifier three-level to two-level modulation;

[0087] Figure 3 This is the block diagram of the linear active disturbance rejection control structure;

[0088] Figure 4 The schematic diagram of the sliding mode auto-disturbance rejection control strategy for the three-phase Vienna rectifier;

[0089] Figure 5 The three-phase current waveform under the fractional-order integral sliding mode active disturbance rejection control strategy in the embodiment of the present invention;

[0090] Figure 6 The three-phase current waveform of the traditional sliding mode anti-disturbance control strategy;

[0091] Figure 7 This is a distortion rate analysis diagram of phase A current under the fractional-order integral sliding mode auto-disturbance rejection control strategy in an embodiment of the present invention;

[0092] Figure 8 This is the distortion rate analysis diagram of phase A current under the traditional sliding mode anti-disturbance control strategy;

[0093] Fig. 9 This is a waveform diagram of the DC bus voltage when the load suddenly increases under the fractional-order integral sliding mode auto-disturbance rejection control strategy in an embodiment of the present invention;

[0094] Fig.10 This is the DC bus voltage waveform diagram of the traditional sliding mode anti-disturbance control strategy with increased load;

[0095] Fig.11 The waveform diagram of three currents on the grid side of a sudden increase in load under the fractional-order integral sliding mode auto-disturbance rejection control strategy in an embodiment of the present invention;

[0096] Fig.12 The waveform diagram of three currents on the grid side under the traditional sliding mode anti-disturbance control strategy when the load suddenly increases;

[0097] Fig.13 This is a flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0098] In order to illustrate the technical solution disclosed by the present invention in detail, the present invention is further clearly and completely described below in conjunction with the accompanying drawings and embodiments.

[0099] Step 1-1: Analyze the topology of Vienna rectifier;

[0100] Figure 1 The figure shows the topological structure of Vienna rectifier, where e sa 、e sb 、e sc is the three-phase voltage of the AC power supply; L a , L b , L c is the AC side energy storage filter inductor. Assume that the three-phase inductors on the AC side are equal, that is, L a =Lb =L c =L; R is the AC side resistance; i a 、i b 、i c is the three-phase current on the AC side; S a , S b , S c It is a combination of three sets of reverse series switch tubes, and its left side is connected to the midpoint of the three sets of diode half bridges; C1 and C2 are DC side capacitors, C1=C2=C, and the upper and lower capacitor voltages are V c1 、V c2 ; Output load is R L , the output current is i R , output voltage V dc =2V c1 =2V c2 . To facilitate subsequent descriptions, it is stipulated that the direction of the three-phase current and voltage from the power supply through the power device and the diode to the DC side is positive. In the Vienna rectifier, the SVPWM vector modulation diagram is usually divided into six sectors based on the flow direction of the three-phase current, and the numbers "1" and "0" are used to represent the conduction and truncation of the power switch tube respectively. In order to facilitate the vector synthesis calculation in the αβ coordinate system, it is necessary to expand the large current sector at the current position outward into a small regular hexagon. At this time, the regular hexagon area can be regarded as a two-level space vector area. Then, the small vector with the center of the regular hexagon pointing to the center of the small regular hexagon of the sector is translated in the opposite direction by the distance of a small vector, so that the starting point of the command voltage is converted from the midpoint of the three-level space to the midpoint of the two-level space, and then it can be converted into a two-level modulation calculation problem. Taking the first sector as an example, the conversion process is as follows Figure 2 shown.

[0101] Step 1-2: Establish the mathematical model of Vienna rectifier;

[0102] When the switch tube is turned on, point a is connected to point N through the power switch tube; when the power switch tube of phase A is cut off, if the current of phase A is positive, the diode of the upper half bridge of the branch is turned on, the diode of the lower half bridge is cut off, and the current of point a is positive relative to point N; conversely, when the current of phase A is negative, the diode of the lower half bridge of the branch is turned on, the diode of the upper half bridge is cut off, and the current of point a is negative relative to point N. That is, each phase arm of the rectifier can be divided into three different modes according to the direction of current flow and the switching state. The switch function group is defined as follows:

[0103]

[0104]

[0105]

[0106] Among them, S ap , S an , S ax They are the equivalent switching states of phase A respectively;

[0107] Based on Kirchhoff's voltage and current theorem, combined with Figure 1 The Vienna rectifier topology structure can be expressed as follows:

[0108]

[0109] Where X = [i a i b i c V c1 V c2 ] T , E=[e sa e sb e sc 00] T ,

[0110] B=diag[1 1 1 0 0],Z=diag[L a L b L c C1 C2]. sa 、e sb 、e sc is the three-phase voltage of the AC power supply; L a , L b , L c is the AC side energy storage filter inductor; V c1 、V c2 are the upper and lower capacitor voltages on the DC side of the Vienna rectifier respectively; L is the three-phase inductance on the AC side; R is the resistance on the AC side; C1 and C2 are the capacitors on the DC side, let C1=C2=C; i a 、i b 、i c is the three-phase current on the AC side;

[0111]

[0112] Since the equation of each phase in the abc coordinate system contains the switching functions of the other two phases, the three-phase variables are coupled with each other. Therefore, it is necessary to convert them into equations in the αβ coordinate system. In the αβ coordinate system, the variables of the controlled object can be reduced, thereby simplifying the design of the control system.

[0113] By performing Clark transformation on equation (4), the Vienna rectifier expression in the αβ coordinate system is:

[0114]

[0115] Among them, S αp , S βp , S αn and S βn is the switch state in the αβ coordinate system; i α and i β is the grid-side current in the αβ coordinate system; e α and e β is the grid-side voltage in the αβ coordinate system; the output current is i R .

[0116] Written in matrix form:

[0117]

[0118] Among them, Z αβ =diag[LL C1 C2],X αβ =[i α i β V c1 V c2 ] T , B αβ =diag[1 1 0 0],E αβ =[e α e β 0 0],

[0119] Step 2-1: According to the instantaneous power theory, the instantaneous power expression can be obtained as:

[0120]

[0121] Among them, P and Q are instantaneous active power and reactive power respectively.

[0122] The voltage on the grid side of the Vienna rectifier can be expressed as:

[0123]

[0124] Where ω is the angular frequency of the AC power supply.

[0125] By taking the derivative of equation (7) and combining equations (6) and (8), the differential expression for instantaneous power is obtained:

[0126]

[0127] Transform the DC side equation in equation (6) so that both sides of the DC side voltage equations are added and multiplied by V dc , we can get the DC side power equation:

[0128]

[0129]

[0130] Among them, P dc is the DC side power, which is the sum of the load power and the power of the two DC energy storage capacitors; V dc is the DC side voltage of Vienna rectifier.

[0131] Step 2-2: Given the grid-side active power and reactive power of the rectifier are P ref , Q ref , the power tracking error can be expressed as:

[0132]

[0133] Wherein, e represents the error vector.

[0134] The designed fractional-order integral sliding mode function is:

[0135] s=e+cD -u e (13)

[0136] Among them, c=diag{c1,c2} is the integral constant matrix, c1>0, c2>0; 0<u<1; s is the sliding mode function; D is the linear operator, and u represents the order of fractional differentiation.

[0137] Select the exponential reaching law:

[0138]

[0139] Among them, ε=diag{ε1, ε2}, ε1>0, ε2>0, k=diag{k1,k2}, k1>0, k2>0.

[0140] The derivative of the sliding surface is:

[0141]

[0142] in,

[0143] From equations (14) and (15), the control law expression of the inner loop controller can be obtained:

[0144] V αβ =M -1 [F+cD 1-u e+ks+εsgn(s)] (16)

[0145] Step 2-3: Analyze the stability of the designed sliding mode control law.

[0146] The Lyapunov equation is selected as follows:

[0147]

[0148] The first-order derivative is:

[0149]

[0150] Let s = [s1 s2] T , then according to equations (13), (14) and (18), we can get:

[0151]

[0152] Because ε1>0, ε2>0, k1>0, k2>0, s1 has the same sign as ε1sgn(s1)+k1s1, and s2 has the same sign as ε2sgn(s2)+k2s2, that is, the sliding surface function s and the sliding surface derivative ds / dt have opposite signs, indicating that the reachability condition of the sliding surface is satisfied, and s1[ε1sgn(s1)+k1s1]+s2[ε2sgn(s2)+k2s2]>0. Therefore, the designed controller can meet the stability requirements.

[0153] Step 3-1: Design linear active disturbance rejection control for the voltage outer loop.

[0154] like Figure 3 The ADRC shown in the figure is an improvement on the PID control, which retains its advantage of not requiring detailed mathematical model information of the controlled object, while solving the contradiction between overshoot and response speed. The linear ADRC is mainly composed of three parts: tracking differentiator TD, linear state error feedback law LSEF and linear extended state observer LESO. ADRC can spontaneously and directly suppress disturbances. In view of the large number of uncertainties, nonlinearities and strong coupling problems in rectifier control, ADRC can estimate the total disturbance in real time through LESO, and then feedforward to offset it, so that the system has strong robustness to disturbances within a certain range.

[0155] Consider the rectifier operating at unity factor, i.e. Q ref =Q=0. Given the DC output voltage is V ref , when the switching loss of the power devices in the circuit and the equivalent impedance loss are ignored, the power consumed on the DC side is equal to the input power on the AC side. The transformation of equation (11) is:

[0156]

[0157] Let y = V ref 2 、f=-4V ref2 / CR L , b=4 / C, u=P, then equation (20) can be transformed into:

[0158]

[0159] Step 3-2: Design of the trace differentiator

[0160] The desired output voltage of the Vienna rectifier is V ref , design the tracking differentiator to make a smooth transition of the control signal to reduce the initial error. For the voltage outer loop, the tracking differentiator is set as:

[0161]

[0162] Among them, r is the adjustable speed factor, which is mainly used to adjust the rising speed during the transition process; v1 is the arranged transition process; v2 is the generalized derivative of v1; V dc is the DC side voltage of Vienna rectifier.

[0163] Step 3-3: Design of Linear Extended State Observer

[0164] The controller input V dc And output u=P ref To estimate and track the various state quantities and total disturbance of the system, we have:

[0165]

[0166] Among them, z1 is the estimate of the DC side voltage; z2 is the estimate of the internal and external disturbances of the rectifier; β1 is an adjustable parameter, and β2 is usually adjusted by expanding the bandwidth of the state observer.

[0167] Step 3-4: Design of linear state error feedback control law

[0168] The error of DC voltage is used as the feedback control quantity, and the disturbance estimation is compensated in real time. The design of LSEF is as follows:

[0169]

[0170] Among them, z1 is the estimation of DC side voltage; z2 is the estimation of internal and external disturbance of rectifier; v1 is the arranged transition process; k s It is an adjustable parameter.

[0171] Therefore, the overall structural principle diagram of the sliding mode anti-disturbance control strategy of the three-phase Vienna rectifier can be obtained as follows: Figure 4 As shown, a PI controller is added to ensure the voltage balance of the upper and lower capacitors.

[0172] In order to verify the correctness and effectiveness of the starting control method based on the improved fractional-order anti-disturbance control designed above, the present invention simulates the Vienna rectifier based on MATLAB / Simulink. First, the fractional-order sliding mode anti-disturbance control strategy designed in this paper is compared with the traditional sliding mode anti-disturbance control strategy to verify the DC bus stability effect under different control strategies. The parameters of the Vienna rectifier simulation model are shown in Table 1. The AC voltage effective value of the generator is set to 230V, the output voltage of the energy storage battery is 200V, and the controller parameters are ε1=ε2=10, k1=k2=35, a1=0.01, a2=15, and a3=100.

[0173] Table 1 Vienna rectifier simulation parameters

[0174]

[0175] Depend on Figure 5 , Figure 6 , Figure 7 , Figure 8 It can be seen that when the traditional sliding mode anti-disturbance control strategy is adopted, the smoothness of the grid-side input current waveform curve is improved, and its total harmonic distortion rate is 3.19%; when the fractional-order integral sliding mode anti-disturbance control strategy is adopted, the grid-side input current waveform is smooth and stable, and the total harmonic distortion rate of the current is 2.24%, which is smaller than the harmonic distortion rate. This shows that the control strategy designed by the present invention is conducive to reducing the input current harmonics and the energy utilization rate of the system is higher.

[0176] The DC bus voltage waveform under load mutation is used to analyze and compare the steady-state and dynamic performance of the designed control strategy. Consider a 50% load increase at 0.1 seconds. Fig. 9 , Fig.10 , Fig.11 , Fig.12 The following are the partial waveforms of DC bus voltage and grid-side three-phase current under the traditional sliding mode anti-disturbance control strategy and the fractional-order integral sliding mode anti-disturbance control strategy. It can be seen from the figure that both control strategies have a good tracking effect on the command voltage in steady state, and the three-phase current waveform distortion rate is small. In the traditional sliding mode anti-disturbance control during the startup process, the overshoot is about 4%, and the voltage drop is about 18V when the load increases suddenly. Under the fractional-order integral sliding mode anti-disturbance control, the overshoot is about 2%, and the voltage drop is about 11V when the load increases suddenly. Through comparative analysis, it can be seen that the fractional-order integral sliding mode anti-disturbance control can make the system have better load disturbance resistance and better dynamic steady-state control effect.

Claims

1. A fractional-order integral sliding mode auto-disturbance rejection control method for Vienna rectifier, characterized in that: The following steps are involved: Step 1: Analyze the topological structure of Vienna rectifier, and establish the mathematical model of Vienna rectifier in three-phase stationary coordinate system and two-phase rotating coordinate system in combination with Kirchhoff's voltage and current theorem; Step 2: Combine sliding mode with fractional-order control for the power inner loop of Vienna rectifier and design a fractional-order integral sliding mode controller; Based on the fractional-order integral sliding surface, active power and reactive power are selected as inner loop control variables, and the established mathematical model is combined with the designed sliding surface to design a fractional-order integral sliding mode control scheme for the power inner loop. Step 3: Design a linear active disturbance rejection control for the voltage outer loop, take the DC side voltage as input and the active power command value as output, design the tracking differentiator, linear extended state observer and linear state error feedback control law respectively, and then obtain the final control law of Vienna rectifier to realize the fractional-order integral sliding mode active disturbance rejection control of Vienna rectifier; In step 1, the mathematical model of the Vienna rectifier is as follows: For the Vienna rectifier, the following assumptions are first made: (1) All power devices, wires, capacitors, inductors, diodes and other devices are lossless ideal devices; (2) The power input voltage is an ideal sine wave, and the input inductor works in a linear state and will not saturate; (3) The switching frequency is much greater than the fundamental frequency of the power supply; The phase current of the Vienna rectifier can flow in both directions in the branch according to the direction of the current when the power switch tube is turned on; when the switch tube is cut off, the current of the branch is zero, that is, the branch is completely disconnected; that is, each phase bridge arm of the rectifier is divided into three different modes according to the direction of current flow and the switching state; the switch function group is defined as follows: Among them, S ap , S an , S ax They are the equivalent switching states of phase A respectively; Based on Kirchhoff's voltage and current theorem and combined with the Vienna rectifier topology, we can obtain the three-phase stationary coordinate system: abc The state equation expression in the coordinate system is: Where X = [i a i b i c V c1 V c2 ] T , E=[e sa e sb e sc 0 0] T , B=diag[1 1 1 0 0], Z=diag[L a L b L c C1 C2]; e sa 、e sb 、e sc is the three-phase voltage of the AC power supply; L a , L b , L c is the AC side energy storage filter inductor; V c1 、V c2 are the upper and lower capacitor voltages on the DC side of the Vienna rectifier respectively; L is the three-phase inductance on the AC side; R is the resistance on the AC side; C1 and C2 are the capacitors on the DC side, let C1=C2=C; i a 、i b 、i c is the three-phase current on the AC side; Among them, R L Output load resistance; By performing Clark transformation on equation (4), the Vienna rectifier expression in the two-phase rotating coordinate system, i.e., the αβ coordinate system, is: Among them, S αp , S βp , S αn , S βn is the switch state in the αβ coordinate system; i α and i β is the grid-side current in the αβ coordinate system; e α and e β is the grid-side voltage in the αβ coordinate system; i R is the output current; Written in matrix form: Among them, Z αβ =diag[LL C1 C2],X αβ =[i α i β V c1 V c2 ] T , B αβ =diag[1 1 0 0], The step 2 includes the following specific steps: Step 2-1: According to the instantaneous power theory, the instantaneous power expression is: Among them, P and Q are instantaneous active power and reactive power respectively; The voltage on the grid side of the Vienna rectifier is expressed as: Where, ω is the angular frequency of the AC power supply; By taking the derivative of equation (7) and combining equations (6) and (8), the differential expression for instantaneous power is obtained: Among them, v α 、v β is the vector voltage; Transform the DC side equation in equation (6) so that both sides of the DC side voltage equations are added and multiplied by V dc , we get the DC side power equation: Among them, P dc is the DC side power, which is the sum of the load power and the power of the two DC energy storage capacitors; V dc is the DC side voltage of Vienna rectifier; Step 2-2: Given the grid-side active power and reactive power of the rectifier are P ref , Q ref , the power tracking error is expressed as: Where, e represents the error vector; The designed fractional-order integral sliding mode function is: s=e+cD -u and (13) Wherein, c=diag{c1,c2} is the integral constant matrix, c1>0, c2>0; 0<u<1; s is the sliding mode function; D is the linear operator, and u represents the order of fractional differential; Select the exponential reaching law: Among them, ε=diag{ε1, ε2}, ε1>0, ε2>0, k=diag{k1,k2}, k1>0, k2>0; The derivative of the sliding surface is: in, The control law expression of the inner loop controller can be obtained from equations (14) and (15): V αβ =M -1 [F+cD 1-u e+ks+εsgn(s)]; (16) The stability of the designed sliding mode control law is analyzed: The Lyapunov equation is selected as follows: The first-order derivative is: Let s = [s1 s2] T , then according to equations (13), (14) and (18), we can obtain: Because ε1>0, ε2>0, k1>0, k2>0, s1 has the same sign as ε1sgn(s1)+k1s1, and s2 has the same sign as ε2sgn(s2)+k2s2, that is, the sliding surface function s and the sliding surface derivative ds / dt have opposite signs, indicating that the reachability condition of the sliding surface is satisfied, and s1[ε1sgn(s1)+k1s1]+s2[ε2sgn(s2)+k2s2]>0. Therefore, the designed controller can meet the stability requirements; The design of linear active disturbance rejection control for the voltage outer loop in step 3 includes the following specific steps: Consider the rectifier operating at unity factor, i.e. Q ref =Q=0; given DC output voltage is V ref ,When the switching loss of the power devices in the circuit and the equivalent impedance loss are ignored, the power consumed on the DC side is equal to the input power on the AC side. The transformation of equation (11) is: Let y = V ref 2 、f=-4V ref 2 / CR L , b=4 / C, u=P, then equation (20) can be transformed into: The design of the tracking differentiator in step 3 includes the following specific steps: The desired output voltage of the Vienna rectifier is V ref , design the tracking differentiator to make a smooth transition of the control signal to reduce the initial error. For the voltage outer loop, the tracking differentiator is set as: Among them, r is the adjustable speed factor, which is mainly used to adjust the rising speed during the transition process; v1 is the arranged transition process; v2 is the generalized derivative of v1; V dc is the DC side voltage of Vienna rectifier; The design of the linear extended state observer in step 3 includes the following specific steps: taking the controller input V dc And output u=P ref To estimate and track the various state quantities and total disturbance of the system, we have: Where z1 is the estimate of the DC side voltage; z2 is the estimate of the internal and external disturbances of the rectifier; β1 is an adjustable parameter, and β2 is usually adjusted by expanding the bandwidth of the state observer; The design of the linear state error feedback control law in step 3 includes the following specific steps: The error of DC voltage is used as the feedback control quantity, and the disturbance estimation is compensated in real time. The design of linear state error feedback law is as follows: Among them, z1 is the estimate of the DC side voltage; z1 is the estimate of the internal and external disturbances of the rectifier; v1 is the lonely process of the arrangement; k s It is an adjustable parameter.

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