Three-phase five-level PWM rectifier based on coupled inductor and integral sliding mode control method

Abstract

The invention discloses a three-phase five-level PWM rectifier based on coupled inductors and an integral sliding mode control method. The rectifier comprises an a-phase PWM rectifier, a b-phase PWM rectifier and a c-phase PWM rectifier with the same topological structure. The control method comprises controlling the three-phase five-level PWM rectifier by adopting a voltage outer loop nonlinear integral sliding mode control, a voltage inner loop PI control and a negative sequence voltage injection method. By adopting a nonlinear integral sliding mode control for the voltage outer loop, the robustness and anti-interference ability of the three-phase five-level PWM rectifier are enhanced, and by adopting a negative sequence voltage injection method, the dynamic response ability of the rectifier system is improved, and the voltage imbalance between phases of the load on the DC side of the three-phase five-level PWM rectifier is suppressed.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular to a three-phase five-level PWM rectifier based on coupled inductors and an integral sliding mode control method. Background Art

[0002] With the development of power electronics technology, pulse width modulation rectifiers have been widely used due to their high power factor operation and bidirectional energy flow. Multilevel rectifiers have the advantages of high output power, low voltage stress, and high power quality. They have great advantages in rail traction and high-voltage direct current transmission systems, especially in high-voltage and high-power applications.

[0003] Three-phase multi-level circuits usually have multiple DC side loads, and the DC side voltage may be unbalanced due to certain line disturbances or parameters. The cascaded H-bridge solves the phase-to-phase voltage problem by using three-level balancing control, intra-phase, inter-phase and global voltage balancing control. Due to the topological characteristics of the three-phase five-level rectifier, there is no need to consider the intra-phase and global voltage balance, only the phase-to-phase voltage needs to be balanced. The mainstream method for phase-to-phase voltage balancing uses zero-sequence voltage injection or negative-sequence voltage injection.

[0004] The performance of PWM rectifier is closely related to its control strategy. Different control strategies have a great impact on the performance of rectifier. PI control is mature and has no steady-state error, but has the problem of poor dynamic performance; sliding mode control (SMC) has the advantages of strong robustness, good dynamic performance, and insensitivity to parameters after the system enters the sliding mode motion. In sliding mode control, the reaching law method is often used to design the control system. Selecting a suitable reaching law can not only make the state variable quickly reach the sliding surface, but also weaken the jitter after reaching the sliding surface. However, in the three-phase multi-level rectifier, the traditional sliding mode control has a certain steady-state error, which affects the working ability of the rectifier. Summary of the invention

[0005] Aiming at the shortcomings of multi-level rectifier control technology, a nonlinear integral sliding mode control method of a three-phase five-level PWM rectifier based on coupled inductors is proposed. The outer loop design adopts nonlinear integral sliding mode control, and the inner loop adopts PI control. In view of the problem of phase-to-phase voltage imbalance due to the existence of multiple DC sides in the three-phase five-level rectifier containing coupled inductors, negative sequence voltage injection is introduced to balance the phase-to-phase voltage. The present invention reduces the control error of the system and suppresses the imbalance of the three-phase output DC voltage.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] The three-phase five-level PWM rectifier based on coupled inductors includes an a-phase PWM rectifier, a b-phase PWM rectifier and a c-phase PWM rectifier with the same topological structure. The a-phase PWM rectifier includes six switch tubes S a1 , S a2 , S a3 , S a4 , S a5 , S a6 , two coupled inductors L a1 and L a2 , a grid-side inductor L sa And the a-phase voltage source u sa , the switch tube S a1 and S a2 After being connected in series, the first bridge arm of phase a is formed. The switch tube S a3 and S a4 After being connected in series, the second bridge arm of phase a is formed. The switch tube S a5 and S a6 After being connected in series, the third bridge arm of phase a is formed. The first bridge arm of phase a, the second bridge arm of phase a and the third bridge arm of phase a form a parallel bridge structure. The coupling inductor L a1 and L a2 After the series connection, both ends are connected to the second bridge arm S of phase a respectively. a3 and S a4 And the third bridge arm S of phase a a5 and S a6 An electrical connection terminal;

[0008] The b-phase PWM rectifier includes six switching tubes S b1 , S b2 , S b3 , S b4 , S b5 , S b6 , two coupled inductors L b1 and L b2 , a grid-side inductor L sb And the b-phase voltage source u sb , the switch tube S b1 and S b2 After being connected in series, the first bridge arm of phase b is formed. The switch tube S b3 and S b4 After being connected in series, the second bridge arm of phase b is formed. The switch tube S b5 and S b6 After being connected in series, the third bridge arm of phase b is formed. The first bridge arm of phase b, the second bridge arm of phase b and the third bridge arm of phase b form a bridge structure connected in parallel with each other. The coupling inductor L b1 and L b2 After the series connection, both ends are connected to the second bridge arm S of phase b. b3 and S b4And the third bridge arm S of phase a b5 and S b6 An electrical connection terminal;

[0009] The c-phase PWM rectifier includes six switch tubes S c1 , S c2 , S c3 , S c4 , S c5 , S c6 , two coupled inductors L c1 and L c2 , a grid-side inductor L sc And the b-phase voltage source u sc , the switch tube S c1 and S c2 After being connected in series, the first bridge arm of phase c is formed. The switch tube S c3 and S c4 After being connected in series, the second bridge arm of phase c is formed. The switch tube S c5 and S c6 After being connected in series, the third bridge arm of phase c is formed. The first bridge arm of phase c, the second bridge arm of phase c and the third bridge arm of phase c form a bridge structure connected in parallel with each other. The coupling inductor L c1 and L c2 After the series connection, both ends are connected to the second bridge arm S of phase c respectively. c3 and S c4 and the third bridge arm S of phase c c5 and S c6 An electrical connection terminal;

[0010] The coupled inductor L a1 and L a2 The series connection ends are respectively connected to the b-phase PWM rectifier coupling inductor L b1 and L b2 The series connection end and the c-phase PWM rectifier coupled inductor L c1 and L c2 The series connection end is electrically connected, and the a-phase first bridge arm switch tube S a1 Emitter and switch tube S a2 The collector is connected through the a-phase grid-side inductor L sa With phase a voltage source u sa One end is electrically connected, and the other end of the a-phase voltage source is electrically connected to the corresponding ends of the b-phase voltage source and the c-phase voltage source respectively.

[0011] The integral sliding mode control method of the three-phase five-level PWM rectifier based on coupled inductors includes controlling the three-phase five-level PWM rectifier by using a voltage outer loop nonlinear integral sliding mode control, a voltage inner loop PI control, and a negative sequence voltage injection method to suppress the inter-phase voltage imbalance of the DC side load of the three-phase five-level PWM rectifier. The control method specifically includes the following steps:

[0012] Based on the single-phase five-level PWM rectifier topology with coupled inductor, it is extended to the three-phase system, and the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductor is established;

[0013] In the abc coordinate system, a mathematical model corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductors is established through the definition of the switching function;

[0014] Perform dq synchronous rotating coordinate system conversion and establish the state equation of the three-phase five-level PWM rectifier based on coupled inductor in the dq synchronous rotating coordinate system;

[0015] A nonlinear integral sliding mode surface is selected, a nonlinear integral sliding mode controller of the three-phase five-level rectifier based on coupled inductance is designed in a dq synchronous rotating coordinate system, a voltage outer loop nonlinear integral sliding mode control is performed on the three-phase five-level PWM rectifier based on coupled inductance, and a given value i of the d-axis current is obtained. d * ;

[0016] The given value of the d-axis current i d * The voltage is transmitted to the inner current loop, and the d-axis voltage command signal and the q-axis voltage command signal in the dq synchronous rotating coordinate system are obtained through PI control;

[0017] The d-axis voltage command signal and the q-axis voltage command signal in the dq synchronous rotating coordinate system are converted into an abc coordinate system to obtain a voltage signal u in the abc coordinate system. a 、u b 、u c ;

[0018] The negative sequence voltage injection method is used to balance the phase voltage. The negative sequence voltage injection method includes: measuring the DC side output voltage u of the three-phase five-level rectifier based on coupled inductance dca 、u dcb and u dcc , the DC side output voltage u dca 、u dcb and u dcc Respectively with u dca 、u dcb and u dcc The mean of the three Make a difference and The negative sequence power P of phase a is obtained by the phase a PI controller, phase b PI controller, and phase c PI controller respectively. na 、b phase negative sequence power P nb and c phase negative sequence power Pnc , and then through Clark transformation, the negative sequence power P in the α and β coordinate systems is obtained α , P β And the three-phase negative sequence voltage u a- 、u b- 、u c- ;

[0019] The three-phase negative sequence voltage u a- 、u b- 、u c- The voltage signal u in the abc coordinate system a 、u b 、u c A linear transformation is performed to obtain a modulated wave signal, which is sent to the modulation module to generate a PWM signal wave to control the corresponding switch tube, thereby completing the control of the three-phase five-level PWM rectifier based on coupled inductors.

[0020] Furthermore, by defining the switching function, ignoring the line resistance and the inductor internal resistance in the main circuit topology, applying KCL and KVL, the mathematical model in the abc coordinate system corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductors is established as shown in formula (1):

[0021]

[0022] In formula (1), u si 、i si Respectively represent the three-phase grid-side voltage and grid-side current, L si is the three-phase grid-side inductance, C i is the DC side capacitance, R i is the load resistance, u dci is the DC side output voltage, S i is the switching state function of the three-phase five-level rectifier circuit defined, i = {a, b, c}.

[0023] According to the control target requirements of achieving unity power factor operation on the grid side and stable output voltage on the DC side of the three-phase five-level PWM rectifier based on coupled inductors, it is necessary to first determine the state equation of the three-phase five-level rectifier in the dq synchronous rotating coordinate system, and then design the control system based on it, in which the outer loop designs a nonlinear integral sliding mode device and the inner loop designs a PI controller.

[0024] Furthermore, the state equation of the three-phase five-level PWM rectifier based on coupled inductors in the dq synchronous rotating coordinate system is shown in equation (2):

[0025]

[0026] In formula (2), u sd 、u sq、i d 、i q is the grid-side voltage and current component in the dq coordinate system, u d 、u q are the components of the input voltage in the dq coordinate system, S d , S q is the input control variable of the mathematical model under the dq coordinate axis, S d Can be used to control the DC side voltage u of a three-phase five-level rectifier dc , S q Can be used to adjust the reactive command current i of the rectifier q , L h is the grid-side inductance in the dq coordinate system, L h ={L sd ,L sq}, C is the DC side capacitance in the dq coordinate system, C={C d ,C q}, R is the DC resistance in the dq coordinate system, R = {R d ,R q}.

[0027] Furthermore, the design steps of the nonlinear integral sliding mode controller include:

[0028] S1: The state equation of the DC side voltage error established in the dq synchronous rotating coordinate system is shown in equation (3):

[0029]

[0030] Simplify formula (3) into formula (4):

[0031]

[0032] In formula (4): A = -1 / CR, u = u dc , B=S d / C,I=i d ;

[0033] S2: Select the nonlinear integral sliding surface as shown in formula (5). Compared with the traditional sliding surface, the nonlinear integral sliding surface can amplify the error and limit the saturation.

[0034] s2=e+a∫f(e)dt (5)

[0035] In formula (5), a is the integral term coefficient, a>0, and the expression of the nonlinear function f(e) is shown in (6):

[0036]

[0037] In formula (6), δ is a positive constant. The main role of δ is that its value will affect the overshoot and dynamic response capability of the system. That is, when δ is too small, the part of the function that amplifies the error will be reduced. When δ is too large, the part of the function that limits saturation will be reduced instead.

[0038] S3: Design the control law according to the nonlinear control theory. The calculation process of the control rate I′ is shown in formula (7):

[0039] I′=I eq ′+I n ′ (7)

[0040] In formula (7), I′ eq is the equivalent control term, I′ n is a discontinuous term, and the calculation process is shown in formula (8):

[0041]

[0042] In formula (8), k is a constant and k>0, sign is a sign function, ε is a constant, 0<ε<1.

[0043] Furthermore, the negative sequence voltage u is obtained a- 、u b- 、u c- The specific steps include:

[0044] S1: Establish a mathematical model of the grid-side voltage and grid-side current when the grid voltage is balanced and does not contain any negative sequence voltage. The mathematical models of the grid-side voltage and grid-side current are shown in equations (9) and (10) respectively:

[0045]

[0046]

[0047] In formula (9), U p , Represents the amplitude and phase angle of the three-phase positive sequence voltage, U n , Represents the amplitude and phase angle of the three-phase negative sequence voltage, U z , Represents the amplitude and phase angle of the three-phase zero-sequence voltage,

[0048] In formula (10), I p , δ p Represents the amplitude and phase angle of the three-phase positive sequence current; I n , δ n Represents the amplitude and phase angle of the three-phase negative sequence current;

[0049] S2: Order u n=ωL si I n , Calculate the negative sequence power generated after the negative sequence component is injected. The negative sequence power P na , P nb , P nc The calculation process of is shown in formula (11):

[0050]

[0051] S3: Perform Clark transformation on equation (11) to obtain the negative sequence power in the α-β coordinate system. The negative sequence power P in the α-β coordinate system is α , P β The calculation process of is shown in formula (12):

[0052]

[0053] S4: Let A = I p cosδ p ,B=I p sinδ p +U p / ωL g , where L g is the grid-side inductance in the α-β coordinate system, L g ={L sα ,L sβ}, find the phase angle and amplitude of the negative sequence voltage injection, the phase angle of the negative sequence voltage injection and amplitude U n The calculation process of is shown in formula (13):

[0054]

[0055] S5: Combine S1 to S4 to calculate the three-phase negative sequence voltage. The three-phase negative sequence voltage u a- 、u b- 、u c- The calculation process of is shown in formula (14):

[0056]

[0057] Furthermore, the modulation module generates a PWM signal wave by adopting a space vector modulation method to control the switch tube S in the a-phase PWM rectifier. a1 , S a2 , S a3 , S a4 , S a5 , S a6 , the switch tube S in the b-phase PWM rectifier b1 , S b2 , Sb3 , S b4 , S b5 , S b6 and the switch tube S in the c-phase PWM rectifier c1 , S c2 , S c3 , S c4 , S c5 , S c6 .

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] 1. The voltage outer loop adopts a nonlinear integral sliding mode controller, which not only enhances the robustness and anti-interference ability of the three-phase five-level PWM rectifier, improves the dynamic response ability of the rectifier system, but also realizes the zero-static error tracking of the rectifier output voltage.

[0060] 2. For the problem of phase-to-phase voltage imbalance caused by the presence of three DC side loads in the rectifier, the negative sequence voltage injection method is used to balance the phase-to-phase voltage. This method is simple to implement, easy to digitize, and has strong practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a topological structure diagram of a three-phase five-level PWM rectifier based on coupled inductors;

[0062] Figure 2 This is a control flow chart of the present invention;

[0063] Figure 3 It is the negative sequence voltage injection flow chart;

[0064] Figure 4 This is the diagram of negative sequence voltage injection combined with inner loop PI;

[0065] Figure 5 This is the input voltage simulation waveform of the three-phase five-level PWM rectifier based on coupled inductors;

[0066] Figure 6 This is the experimental diagram of the steady-state grid-side voltage and current of phase A of the three-phase five-level PWM rectifier based on coupled inductors;

[0067] Figure 7 This is the experimental diagram of the DC side starting voltage of the three-phase five-level PWM rectifier with integral sliding mode based on coupled inductors;

[0068] Figure 8 This is the experimental diagram of the DC side voltage of the three-phase five-level PWM rectifier based on coupled inductors with integrated sliding mode and sudden increase of DC side resistance;

[0069] Fig. 9This is the experimental diagram of the DC side voltage increase of the three-phase five-level PWM rectifier with integral sliding mode given voltage based on coupled inductors;

[0070] Fig.10 This is the experimental diagram of the DC side voltage waveform before and after the negative sequence voltage is injected; DETAILED DESCRIPTION

[0071] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the invention, all other embodiments obtained by ordinary technicians in this field without creative work, any modifications, equivalent substitutions, improvements, etc., should be included in the protection scope of the present invention.

[0072] like Figure 1 As shown, the three-phase five-level PWM rectifier based on coupled inductors includes an a-phase PWM rectifier, a b-phase PWM rectifier and a c-phase PWM rectifier with the same topological structure, wherein the a-phase PWM rectifier includes six switch tubes S a1 , S a2 , S a3 , S a4 , S a5 , S a6 , two coupled inductors L a1 and L a2 , a grid-side inductor L sa And the a-phase voltage source u sa , the switch tube S a1 and S a2 After being connected in series, the first bridge arm of phase a is formed. The switch tube S a3 and S a4 After being connected in series, the second bridge arm of phase a is formed. The switch tube S a5 and S a6 After being connected in series, the third bridge arm of phase a is formed. The first bridge arm of phase a, the second bridge arm of phase a and the third bridge arm of phase a form a parallel bridge structure. The coupling inductor L a1 and L a2 After the series connection, both ends are connected to the second bridge arm S of phase a respectively. a3 and S a4 And the third bridge arm S of phase a a5 and S a6 An electrical connection terminal;

[0073] The b-phase PWM rectifier includes six switching tubes S b1 , S b2 , S b3 , S b4 , S b5 , S b6, two coupled inductors L b1 and L b2 , a grid-side inductor L sb And the b-phase voltage source u sb , the switch tube S b1 and S b2 After being connected in series, the first bridge arm of phase b is formed. The switch tube S b3 and S b4 After being connected in series, the second bridge arm of phase b is formed. The switch tube S b5 and S b6 After being connected in series, the third bridge arm of phase b is formed. The first bridge arm of phase b, the second bridge arm of phase b and the third bridge arm of phase b form a bridge structure connected in parallel with each other. The coupling inductor L b1 and L b2 After the series connection, both ends are connected to the second bridge arm S of phase b. b3 and S b4 And the third bridge arm S of phase a b5 and S b6 An electrical connection terminal;

[0074] The c-phase PWM rectifier includes six switch tubes S c1 , S c2 , S c3 , S c4 , S c5 , S c6 , two coupled inductors L c1 and L c2 , a grid-side inductor L sc And the b-phase voltage source u sc , the switch tube S c1 and S c2 After being connected in series, the first bridge arm of phase c is formed. The switch tube S c3 and S c4 After being connected in series, the second bridge arm of phase c is formed. The switch tube S c5 and S c6 After being connected in series, the third bridge arm of phase c is formed. The first bridge arm of phase c, the second bridge arm of phase c and the third bridge arm of phase c form a bridge structure connected in parallel with each other. The coupling inductor L c1 and L c2 After the series connection, both ends are connected to the second bridge arm S of phase c respectively. c3 and S c4 and the third bridge arm S of phase c c5 and S c6 An electrical connection terminal;

[0075] The coupled inductor L a1 and L a2 The series connection ends are respectively connected to the b-phase PWM rectifier coupling inductor L b1 and L b2The series connection end and the c-phase PWM rectifier coupled inductor L c1 and L c2 The series connection end is electrically connected, and the a-phase first bridge arm switch tube S a1 Emitter and switch tube S a2 The collector is connected through the a-phase grid-side inductor L sa With phase a voltage source U sa One end is electrically connected, and the other end of the a-phase voltage source is electrically connected to the corresponding ends of the b-phase voltage source and the c-phase voltage source respectively.

[0076] like Figure 2 As shown, the integral sliding mode control method of the three-phase five-level PWM rectifier based on coupled inductors includes controlling the three-phase five-level PWM rectifier by adopting a voltage outer loop nonlinear integral sliding mode control, a voltage inner loop PI control and a negative sequence voltage injection method to suppress the inter-phase voltage imbalance of the DC side load of the three-phase five-level PWM rectifier. The control method specifically includes the following steps:

[0077] Based on the single-phase five-level PWM rectifier topology with coupled inductor, it is extended to the three-phase system, and the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductor is established;

[0078] In the abc coordinate system, a mathematical model corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductors is established through the definition of the switching function;

[0079] Perform dq synchronous rotating coordinate system conversion and establish the state equation of the three-phase five-level PWM rectifier based on coupled inductance in the dq synchronous rotating coordinate system;

[0080] A nonlinear integral sliding mode surface is selected, a nonlinear integral sliding mode controller of the three-phase five-level rectifier based on coupled inductance is designed in a dq synchronous rotating coordinate system, a voltage outer loop nonlinear integral sliding mode control is performed on the three-phase five-level PWM rectifier based on coupled inductance, and a given value i of the d-axis current is obtained. d * ;

[0081] The given value of the d-axis current i d * The voltage is transmitted to the inner current loop, and the d-axis voltage command signal and the q-axis voltage command signal in the dq synchronous rotating coordinate system are obtained through PI control;

[0082] The d-axis voltage command signal and the q-axis voltage command signal in the dq synchronous rotating coordinate system are converted into an abc coordinate system to obtain a voltage signal u in the abc coordinate system. a 、u b 、u c ;

[0083] like Figure 3 As shown, a negative sequence voltage injection method is used to balance the phase voltage. The negative sequence voltage injection method includes: measuring the DC side output voltage u of the three-phase five-level rectifier based on coupled inductance dca 、u dcb and u dcc , the DC side output voltage u dca 、u dcb and u dcc Respectively with u dca 、u dcb and u dcc The mean of the three Make a difference and The negative sequence power P of phase a is obtained by the phase a PI controller, phase b PI controller, and phase c PI controller respectively. na 、b phase negative sequence power P nb and c phase negative sequence power P nc , and then through Clark transformation, the negative sequence power P in the α and β coordinate systems is obtained α , P β And the three-phase negative sequence voltage u a- 、u b- 、u c- ;

[0084] like Figure 4 As shown, the three-phase negative sequence voltage u a- 、u b- 、u c- The voltage signal u in the abc coordinate system a 、u b 、u c A linear transformation is performed to obtain a modulated wave signal, which is sent to the modulation module to generate a PWM signal wave to control the corresponding switch tube, thereby completing the control of the three-phase five-level PWM rectifier based on coupled inductors.

[0085] By defining the switching function, ignoring the line resistance and the inductor internal resistance in the main circuit topology, applying KCL and KVL, the mathematical model in the abc coordinate system corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductors is established as shown in formula (1):

[0086]

[0087] In formula (1), u si 、i si Respectively represent the three-phase grid-side voltage and grid-side current, L si is the three-phase grid-side inductance, C i is the DC side capacitance, R i is the load resistance, udci is the DC side output voltage, S i is the switching state function of the three-phase five-level rectifier circuit defined, i = {a, b, c}.

[0088] According to the control target requirements of achieving unity power factor operation on the grid side and stable output voltage on the DC side of the three-phase five-level PWM rectifier based on coupled inductors, it is necessary to first determine the state equation of the three-phase five-level rectifier in the dq synchronous rotating coordinate system, and then design the control system based on it, in which the outer loop designs a nonlinear integral sliding mode device and the inner loop designs a PI controller.

[0089] The state equation of the three-phase five-level PWM rectifier based on coupled inductors in the dq synchronous rotating coordinate system is shown in equation (2):

[0090]

[0091] In formula (2), u sd 、u sq 、i d 、i q is the grid-side voltage and current component in the dq coordinate system, u d 、u q are the components of the input voltage in the dq coordinate system. d , S q is the input control variable of the mathematical model under the dq coordinate axis, S d Can be used to control the DC side voltage u of a three-phase five-level rectifier dc , S q Can be used to adjust the reactive command current i of the rectifier q , L h is the grid-side inductance in the dq coordinate system, L h ={L sd ,L sq}, C is the DC side capacitance in the dq coordinate system, C={C d ,C q}, R is the DC resistance in the dq coordinate system, R = {R d ,R q}.

[0092] The design steps of the nonlinear integral sliding mode controller include:

[0093] S1: The state equation of the DC side voltage error established in the dq synchronous rotating coordinate system is shown in equation (3):

[0094]

[0095] Simplify formula (3) into formula (4):

[0096]

[0097] In formula (4): A = -1 / CR, u = u dc , B=S d / C,I=i d ;

[0098] S2: Select the nonlinear integral sliding surface as shown in formula (5). Compared with the traditional sliding surface, the nonlinear integral sliding surface can amplify the error and limit the saturation.

[0099] s2=e+a∫f(e)dt (5)

[0100] In formula (5), a is the integral term coefficient, a>0, and the expression of the nonlinear function f(e) is shown in (6):

[0101]

[0102] In formula (6), δ is a positive constant. The main function of δ is that its value will affect the overshoot and dynamic response capability of the system. That is, when δ is too small, the part of the function that amplifies the error will be reduced. When δ is too large, the part of the function that limits saturation will be reduced. The preferred value is: 2≤δ≤5;

[0103] S3: Design the control law according to the nonlinear control theory. The calculation process of the control rate I′ is shown in formula (7):

[0104] I′=I eq ′+I n ′ (7)

[0105] In formula (7), I′ eq is the equivalent control term, I′ n is a discontinuous term, and the calculation process is shown in formula (8):

[0106]

[0107] In formula (8), k is a constant and k>0, sign is a sign function, ε is a constant, 0<ε<1.

[0108] Get the three-phase negative sequence voltage u a- 、u b- 、u c- The specific steps include:

[0109] S1: Establish a mathematical model of the grid-side voltage and grid-side current when the grid voltage is balanced and does not contain any negative sequence voltage. The mathematical models of the grid-side voltage and grid-side current are shown in equations (9) and (10) respectively:

[0110]

[0111]

[0112] In formula (9), U p , Represents the amplitude and phase angle of the three-phase positive sequence voltage, U n , Represents the amplitude and phase angle of the three-phase negative sequence voltage; U z , Represents the amplitude and phase angle of the three-phase zero-sequence voltage,

[0113] In formula (10), I p , δ p Represents the amplitude and phase angle of the three-phase positive sequence current, I n , δ n Represents the amplitude and phase angle of the three-phase negative sequence current;

[0114] S2: Order u n =ωL si I n , Calculate the negative sequence power generated after the negative sequence component is injected. The negative sequence power P na , P nb , P nc The calculation process of is shown in formula (11):

[0115]

[0116] S3: Perform Clark transformation on equation (11) to obtain the negative sequence power in the α-β coordinate system. The negative sequence power P in the α-β coordinate system is α , P β The calculation process of is shown in formula (12):

[0117]

[0118] S4: Let A = I p cosδ p ,B=I p sinδ p +U p / ωL g , where L g is the grid-side inductance in the α-β coordinate system, L g ={L sα ,L sβ}, find the phase angle and amplitude of the negative sequence voltage injection, the phase angle of the negative sequence voltage injection and amplitude U n The calculation process of is shown in formula (13):

[0119]

[0120] S5: Combine S1 to S4 to calculate the three-phase negative sequence voltage. The three-phase negative sequence voltage u a- 、u b- 、u c- The calculation process of is shown in formula (14):

[0121]

[0122] The modulation module generates a PWM signal wave by adopting a space vector modulation method to control the switch tube S in the a-phase PWM rectifier. a1 , S a2 , S a3 , S a4 , S a5 , S a6 , the switch tube S in the b-phase PWM rectifier b1 , S b2 , S b3 , S b4 , S b5 , S b6 and the switch tube S in the c-phase PWM rectifier c1 , S c2 , S c3 , S c4 , S c5 , S c6 .

[0123] In order to verify the effect of the outer loop of the present invention using integral sliding mode control and introducing negative sequence voltage injection to balance the phase voltage, a semi-physical experimental simulation platform based on TMS302-F28335DSP and RT-lab was built, and a three-phase five-level rectifier main circuit with coupled inductors was built on the experimental simulation platform, and a simulation experiment was carried out to verify the integral sliding mode control algorithm.

[0124] In this experiment, the preferred main circuit simulation parameters are shown in Table 1. This experiment compares the dual PI control algorithm, the traditional power reaching law sliding mode + PI control algorithm and the integral sliding mode + PI control algorithm adopted by the present invention, and compares the DC side voltage waveforms before and after the injection of negative sequence voltage based on the integral sliding mode + PI control.

[0125] Table 1 Simulation parameters

[0126]

[0127] like Figure 5As shown, it is the input side voltage waveform of the three-phase five-level PWM rectifier circuit based on coupled inductance designed by the present invention. It can be seen that the three-phase input side voltages are all five-level, and the phase difference between the voltages is 120°.

[0128] like Figure 6 As shown, this is the voltage and current waveform of the grid side of phase A under the control of the integral sliding mode algorithm. It can be seen that the grid side voltage and current of phase A achieve high power factor operation.

[0129] Figure 7 The DC voltage waveform diagram of the startup process of the three control algorithms: the dual PI control algorithm, the traditional power reaching law sliding mode + PI control algorithm, and the integral sliding mode + PI control algorithm adopted by the present invention. Figure 7 As can be seen from (a), compared with the other two control methods, the PI control is slower and takes longer to start, and it takes about 300ms to reach a stable state. Although the steady-state error of this control method is small, there is a large overshoot. Figure 7 As can be seen from (b), the time it takes to reach stability using traditional sliding mode control is about 120ms, and the overshoot is small. Not only does it fail to achieve zero-static-error tracking of the output voltage, but it also has a certain steady-state error. Figure 7 As can be seen from (c), the time taken to reach the stable process using integral sliding mode control is about 120ms, and the overshoot is relatively low, which not only retains the starting speed of the sliding mode control itself, but also achieves zero-static-error tracking.

[0130] like Figure 8 The figure shows the DC voltage change diagram when the resistance suddenly increases when using the dual PI control algorithm, the traditional power approaching sliding mode + PI control algorithm, and the integral sliding mode + PI control algorithm used in the present invention. The resistance changes from 30Ω to 35Ω. Figure 8 As can be seen from (a), compared with the other two control methods, the PI control takes a longer time to recover stability, about 120ms. At the same time, although the steady-state error of this control method is small, the DC side voltage fluctuates greatly. Figure 8 As can be seen from (b), the voltage waveform of the traditional sliding mode control basically does not change before and after the jump, but the output voltage is not tracked without static error during the startup and recovery process, and there is a certain steady-state error. Figure 8 As can be seen from (c), the time taken for re-stabilization using integral sliding mode control is about 40ms, and the voltage fluctuation on the DC side is relatively low, which not only retains the dynamic capability of traditional sliding mode control, but also ensures that the output voltage has no steady-state error.

[0131] like Fig. 9The given voltage sudden change DC side voltage waveform is shown in the startup process of the three control algorithms: the dual PI control algorithm, the traditional power approaching law sliding mode + PI control algorithm, and the integral sliding mode + PI control algorithm adopted by the present invention. The given voltage changes from 500V to 550V. Fig. 9 As can be seen from (a), compared with the other two control methods, PI control takes about 160ms to recover stability, the recovery process takes longer, and the steady-state error is smaller; Fig. 9 As can be seen from (b), the dynamic capability of the traditional sliding mode control is relatively strong, and the restabilization time is about 50ms, but the output voltage tracking without static error is still not achieved; Fig. 9 As can be seen from (c), it takes 100ms to reach the stable process using the integral sliding mode, and the steady-state error is small. It can be seen that the use of integral sliding mode control retains the dynamic capability of traditional sliding mode control and realizes zero-static error tracking of the output voltage.

[0132] like Fig.10 (a) shows the DC side voltage waveform when the integral sliding mode control algorithm does not inject negative sequence voltage. A sudden load change is designed at 500ms, and the resistance of phase A is suddenly changed from 30Ω to 35Ω, while the resistances of the other two phases remain unchanged, in order to simulate the unbalanced three-phase load. It can be seen from the figure that when the negative sequence voltage is not injected, the startup is carried out under load balance conditions. During the startup process, there are differences in the three-phase DC side voltages. After adjustment, the three-phase voltage waveforms tend to be balanced. After the 500ms load mutation, the phase-to-phase voltage is obviously unbalanced.

[0133] like Fig.10 (b) shows the DC side voltage waveform with negative sequence voltage injected under the control algorithm. It can be seen from the figure that after the negative sequence voltage is injected, the voltage waveform can be basically consistent during the startup process, and it can still maintain balance after a phase load jump occurs. It can be seen that injecting negative sequence voltage can suppress the imbalance of phase voltage and maintain the balance of the three-phase DC side output voltage.

[0134] The present invention combines the advantages of sliding mode control and proportional integral control. The proposed integral sliding mode control algorithm improves the robustness, anti-interference ability and dynamic response of the three-phase five-level PWM rectifier based on coupled inductance designed by the present invention, while realizing the error-free tracking of the output voltage command; in addition, in order to solve the problem of unbalanced load voltage on the three-phase DC side, the phase-to-phase voltage is balanced by combining the method of negative sequence voltage injection, which has strong practicality.

Claims

1. A three-phase five-level PWM rectifier based on coupled inductors, characterized in that: The three-phase five-level PWM rectifier based on coupled inductors comprises an a-phase PWM rectifier, a b-phase PWM rectifier and a c-phase PWM rectifier with the same topological structure, the a-phase PWM rectifier comprises a first switch tube, a second switch tube, a third switch tube, a fourth switch tube, a fifth switch tube, a sixth switch tube, a first coupled inductor, a second coupled inductor, a grid-side inductor and an a-phase voltage source, the first switch tube and the second switch tube, the third switch tube and the fourth switch tube, the fifth switch tube and the sixth switch tube, respectively, are connected in series with emitters and collectors in pairs to form a first bridge arm of the a-phase, a second bridge arm of the a-phase and a third bridge arm of the a-phase connected in parallel, the The same-name end of the first coupled inductor is electrically connected to the emitter of the third switch tube and the collector of the fourth switch tube respectively, and the opposite-name end of the second coupled inductor is electrically connected to the emitter of the fifth switch tube and the collector of the sixth switch tube respectively; the opposite-name end of the first coupled inductor and the same-name end of the second coupled inductor are electrically connected in series with the corresponding coupled inductor series connection ends of the b-phase PWM rectifier and the c-phase PWM rectifier respectively, and the emitter of the first switch tube and the collector of the second switch tube on the first bridge arm of the a-phase are electrically connected to one end of the a-phase voltage source through the a-phase grid-side inductor, and the other end of the a-phase voltage source is electrically connected to the corresponding ends of the b-phase voltage source and the c-phase voltage source respectively; An integral sliding mode control method for a three-phase five-level PWM rectifier based on coupled inductors includes controlling the three-phase five-level PWM rectifier by using a voltage outer loop nonlinear integral sliding mode control, a voltage inner loop PI control, and a negative sequence voltage injection method to suppress the inter-phase voltage imbalance of the DC side load of the three-phase five-level PWM rectifier. The control method specifically includes the following steps: Based on the single-phase five-level PWM rectifier topology with coupled inductor, it is extended to the three-phase system, and the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductor is established; exist abc In the coordinate system, a mathematical model corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductors is established through the definition of the switching function; conduct dq Synchronous rotating coordinate system conversion, establish a three-phase five-level PWM rectifier based on coupled inductors dq State equations in synchronously rotating coordinate systems; Select the nonlinear integral sliding surface and design the three-phase five-level rectifier based on coupled inductance. dq A nonlinear integral sliding mode controller in a synchronous rotating coordinate system performs a voltage outer loop nonlinear integral sliding mode control on the three-phase five-level PWM rectifier based on coupled inductance to obtain d The given value of shaft current; The d The given value of the shaft current is passed to the current inner loop and obtained through PI control dq Synchronous rotating coordinate system d The shaft voltage command signal and q Shaft voltage command signal; Regarding the dq Synchronous rotating coordinate system d The shaft voltage command signal and q The shaft voltage command signal is abc Coordinate system conversion, obtain abc Voltage signal in the coordinate system; The negative sequence voltage injection method is used to balance the phase voltage. The negative sequence voltage injection method includes: measuring the output voltage of each phase on the DC side of the three-phase five-level rectifier based on coupled inductance, subtracting the output voltage of each phase on the DC side from the average of the output voltage of each phase, and obtaining the negative sequence power of each phase through the PI controller of each phase, and then obtaining the negative sequence power through Clark transformation. and Negative sequence power and negative sequence voltage of each phase in the coordinate system; The negative sequence voltage of each phase and the abc The voltage signal in the coordinate system is linearly transformed to obtain a modulation wave signal, which is sent to the modulation module to generate a PWM signal wave to control the corresponding switch tubes in the a-phase PWM rectifier, the b-phase PWM rectifier and the c-phase PWM rectifier, thereby completing the control of the three-phase five-level PWM rectifier based on coupled inductors.

2. The three-phase five-level PWM rectifier integral sliding mode control method based on coupled inductance according to claim 1 is characterized in that: Corresponding to the main circuit topology of the three-phase five-level PWM rectifier based on coupled inductance abc The mathematical model in the coordinate system is shown in formula (1): (1) In formula (1), , Respectively represent the three-phase grid-side voltage and grid-side current, is the three-phase grid-side inductance, is the DC side capacitance, is the load resistance, is the DC side output voltage, is the switch state function of the three-phase five-level rectifier circuit defined, .

3. The three-phase five-level PWM rectifier integral sliding mode control method based on coupled inductance according to claim 2 is characterized in that: Three-phase five-level PWM rectifier based on coupled inductor dq The state equation in the synchronous rotating coordinate system is shown in equation (2): （2） In formula (2), , , , The grid side voltage and current are dq The components in the coordinate system, , The input voltage is d - q The components in the coordinate system, , for dq The input control variables of the mathematical model under the coordinate axis, Can be used to control the DC side voltage of a three-phase five-level rectifier , Can be used to adjust the reactive command current of the rectifier ; In formula (2), yes dq The grid-side inductance in the coordinate system, , yes dq The DC link capacitance in the coordinate system, , yes dq The DC resistance in the coordinate system, .

4. The three-phase five-level PWM rectifier integral sliding mode control method based on coupled inductance according to claim 3 is characterized in that: The design steps of the nonlinear integral sliding mode controller include: S1: Built on dq The state equation of the DC side voltage error in the synchronous rotating coordinate system is shown in equation (3): （3） Simplify formula (3) into formula (4): （4） In formula (4): , , , ; S2: Select the nonlinear integral sliding surface as shown in formula (5); （5） In formula (5), a is the integral term coefficient, a > 0, nonlinear function f ( e ) is expressed as (6): （6） S3: Design control law based on nonlinear control theory. The calculation process of is shown in formula (7): （7） In formula (7), is an equivalent control term, is a discontinuous term, and the calculation process is shown in formula (8): （8） In formula (8), k is a constant and k>0 , sign is the symbolic function, is a constant, 0< <1.

5. The three-phase five-level PWM rectifier integral sliding mode control method based on coupled inductance according to claim 4 is characterized in that: The specific steps of obtaining the negative sequence voltage of each phase include: S1: Establish a mathematical model of the grid-side voltage and grid-side current when the grid voltage is balanced and does not contain any negative sequence voltage. The mathematical models of the grid-side voltage and grid-side current are shown in equations (9) and (10) respectively: （9） （10） In formula (9), , Represents the amplitude and phase angle of the three-phase positive sequence voltage, , Represents the amplitude and phase angle of the three-phase negative sequence voltage, , Represents the amplitude and phase angle of the three-phase zero-sequence voltage; In formula (10), , Represents the amplitude and phase angle of the three-phase positive sequence current, , Represents the amplitude and phase angle of the three-phase negative sequence current; S2: Order , , , calculate the negative sequence power generated after the negative sequence component is injected, the negative sequence power of each phase , , The calculation process of is shown in formula (11): （11） S3: Perform Clark transformation on equation (11) to obtain α - β The negative sequence power in the coordinate system is α - β Negative sequence power in the coordinate system , The calculation process of is shown in formula (12): （12） S4: Order , ,in yes α - β The grid-side inductance in the coordinate system, , find the phase angle and amplitude of the negative sequence voltage injection, the phase angle of the negative sequence voltage injection and amplitude The calculation process of is shown in formula (13): （13） S5: Combine S1~S4 to calculate the negative sequence voltage of each phase. 、 , The calculation process of is shown in formula (14): （14）。 6. The three-phase five-level PWM rectifier integral sliding mode control method based on coupled inductance according to claim 5, characterized in that: The modulation module generates PWM signal waves by adopting a space vector modulation method to respectively control the switch tubes in the a-phase PWM rectifier, the b-phase PWM rectifier and the c-phase PWM rectifier.

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