Mapping Adaptive Backstepping Sliding Mode Control Method for LCL-Type Photovoltaic Grid-Connected Inverters

Abstract

The present invention discloses a mapping adaptive backstepping sliding mode control method for an LCL-type photovoltaic grid-connected inverter, which relates to the technical field of grid-connected inverter control. First, an LCL-type photovoltaic grid-connected inverter system is built. According to the LCL-type photovoltaic grid-connected inverter, the state equation of the grid-connected inverter is determined. Then, based on the state equation of the grid-connected inverter, a precise linearized standard state equation is obtained. Furthermore, according to the precise linearized standard state equation, a sliding mode controller for the LCL-type photovoltaic grid-connected inverter based on the Lyapunov stability theorem is designed by using the backstepping method, and the control law of the backstepping sliding mode system is designed based on the sliding mode controller. Finally, an adaptive backstepping sliding mode control law is designed by combining the mapping adaptive algorithm with the control law of the backstepping sliding mode system. The present invention ensures the asymptotic stability of the LCL-type photovoltaic grid-connected inverter system, improves the dynamic performance, robust performance and self-adaptability of the system, and enables the system to have good dynamic characteristics and strong anti-interference ability.

Description

Technical Field

[0001] The present invention belongs to the technical field of grid-connected inverter control, and particularly relates to a mapping adaptive backstepping sliding mode control method for an LCL-type photovoltaic grid-connected inverter. Background Art

[0002] With the rapid development of distributed energy, the operation of photovoltaic power generation systems in the form of microgrids connected to large power grids is the main direction of future technological development and an important measure to increase the scale of photovoltaic power generation. As a key interface device for photovoltaic power generation systems to be connected to the grid, the grid-connected inverter is used to convert direct current into alternating current that meets the requirements of the commercial power grid, and thus is widely used in the field of distributed energy.

[0003] Compared with traditional L-type grid-connected inverters, LCL-type grid-connected inverters have good ability to suppress high-frequency harmonics, but their inherent resonance problems will affect the stability of the system. In order to eliminate the resonance problem, it can be suppressed by two methods: passive damping and active damping. Passive damping will cause energy loss in the photovoltaic grid-connected inverter system, and active damping realizes the suppression of resonance through algorithms. However, in actual operation, the parameters of the filter often drift with the change of external conditions, and the influence of the grid impedance in the case of a weak grid will cause the actual resonance point to shift, resulting in the failure of the traditional active damping method. In order to cope with the uncertainty of the model and the interference of external factors, it is required that the grid-connected inverter system has strong anti-interference ability and robustness.

[0004] In recent years, the grid-connected current control of grid-connected inverters mainly uses classical PID and PR controllers, and observer and other control methods are introduced on this basis. However, these control methods have relatively high requirements for the accuracy of the system model, and it is difficult to obtain an accurate model in actual operation, so the tracking accuracy is greatly reduced. Summary of the Invention

[0005] Aiming at the above problems, the present invention provides a mapping adaptive backstepping sliding mode control method for an LCL-type photovoltaic grid-connected inverter. First, an LCL-type photovoltaic grid-connected inverter system is built. The state equation of the grid-connected inverter is determined according to the LCL-type photovoltaic grid-connected inverter. Then, the exact linearized standard state equation is obtained through the state equation of the grid-connected inverter. Next, based on the exact linearized standard state equation, a sliding mode controller for the LCL-type photovoltaic grid-connected inverter is designed by using the backstepping method based on the Lyapunov stability theorem, and the control law of the backstepping sliding mode system is designed according to the sliding mode controller. Finally, the adaptive backstepping sliding mode control law is designed by combining the mapping adaptive algorithm with the control law of the backstepping sliding mode system. Among them, by recursively constructing the Lyapunov function of the closed-loop system, the asymptotic stability of the LCL-type photovoltaic grid-connected inverter system is guaranteed, and the structurization of the controller design is realized. The backstepping method ensures the Lyapunov stability of the LCL-type photovoltaic grid-connected inverter system, and on this basis, sliding mode control is adopted to improve the dynamic performance and robustness of the LCL-type photovoltaic grid-connected inverter system. In particular, the switching gain in the sliding mode reaching law is obtained through the mapping adaptive law, so the self-adaptability of the LCL-type photovoltaic grid-connected inverter system is improved. The present invention can not only ensure the global stability of the system, but also has good robustness against the uncertain changes caused by the system model parameters and external disturbances, improves the tracking accuracy of the grid-connected current, and effectively solves the existing technical problems.

[0006] The technical solution adopted by the present invention:

[0007] A mapping adaptive backstepping sliding mode control method for an LCL-type photovoltaic grid-connected inverter, characterized by comprising the following steps:

[0008] S1. Build an LCL-type photovoltaic grid-connected inverter system;

[0009] S2. Determine the state equation of the grid-connected inverter according to the LCL-type photovoltaic grid-connected inverter;

[0010] S3. Obtain the exact linearized standard state equation through the state equation of the grid-connected inverter;

[0011] S4. According to the exact linearized standard state equation, design a sliding mode controller for the LCL-type photovoltaic grid-connected inverter by using the backstepping method based on the Lyapunov stability theorem, and then design the control law of the backstepping sliding mode system according to the sliding mode controller;

[0012] S5. Design the adaptive backstepping sliding mode control law by combining the mapping adaptive algorithm with the control law of the backstepping sliding mode system;

[0013] The design of the adaptive backstepping sliding mode control law by using the mapping adaptive algorithm includes the selection of the sliding mode reaching law: Wherein is the sliding mode reaching law, s is the sliding mode surface, c is the sliding mode surface coefficient, ε is the switching gain of the sliding mode surface. The switching gain ε is selected to calculate the mapping adaptive algorithm, which specifically includes:

[0014] Through the design of the adaptive law, the estimated value of the switching gain ε varies within [ε min , ε max . When , where λ is a coefficient,

[0015]

[0016] When is greater than or equal to the maximum value ε max , if there is a tendency to continue increasing, that is, then the value is unchanged. When is less than or equal to the minimum value ε min , if there is a tendency to continue decreasing, that is, then the value is unchanged. That is, the design of the adaptive law ensures that the estimated value of the switching gain varies within [ε min , ε max .

[0017] Preferably, it also includes using the Lyapunov function to verify the stability of the controller.

[0018] Preferably, the state equation of the grid-connected inverter is represented by the Brunovsky canonical form of the grid-connected inverter in the Z space:

[0019]

[0020] In the above formula, z1, z2, and z3 are the state variables in the Z space, y is the output variable, v is the control input in the Z space, is the first derivative of the state variable in the Z space.

[0021] Preferably, the exact linearized standard state equation is obtained according to the state equation of the grid-connected inverter, which specifically includes:

[0022] The nonlinear control law in the X space is calculated according to the state equation of the grid-connected inverter:

[0023]

[0024] In the above formula, the state variables in the X space are: The input quantity is the duty cycle u, U inis a DC input power supply, L1 is the output inductor on the inverter side, L2 is the filter inductor on the grid side, C is the filter capacitor, and R L is the load, v is the control input in the Z space, i1 is the current on the inverter side, and u c is the voltage of the filter capacitor, and i g is the grid-connected current;

[0025] Considering the uncertain changes caused by the error between the actual value and the true value of the filter parameters, the nonlinear control law equation in the X space is rewritten as the standard state equation of exact linearization, and the standard state equation of exact linearization is:

[0026]

[0027] In the above formula, is the first derivative of the state variable in the Z space, is the total disturbance.

[0028] Preferably, according to the standard state equation of exact linearization, a sliding mode controller for the LCL-type photovoltaic grid-connected inverter based on the Lyapunov stability theorem is designed by the backstepping method, and then the control law of the backstepping sliding mode system is designed based on the sliding mode controller, specifically including:

[0029] The control objective of the exact linearization model is to control the state variable z1 to track its reference value z d , according to the backstepping principle, the tracking error e1 is defined as the difference between z1 and z d :

[0030]

[0031] Set the Lyapunov energy function F1:

[0032] Set the Lyapunov energy function F2: e2 is the intermediate virtual control quantity;

[0033] Set the Lyapunov energy function F3: e3 is the intermediate virtual control quantity;

[0034] The control law of the backstepping sliding mode system is:

[0035]

[0036] where k1 and k2 are the coefficients of the Lyapunov energy function.

[0037] Preferably, the Lyapunov function is used to verify the stability of the sliding mode controller, specifically including:

[0038] According to the principle of the LCL-type photovoltaic grid-connected inverter, the fluctuations of the inductor parameters and capacitor parameters are limited within one cycle. Therefore, the total disturbance is an uncertain factor but bounded. Let K be the maximum value of the total disturbance range. When the control parameter ε ≥ K and the derivative of the Lyapunov energy function F3 ≤ 0, the sliding mode controller is stable; otherwise, it is unstable.

[0039] Preferably, the derivative of the Lyapunov energy function F3 ≤ 0 is expressed as:

[0040]

[0041] In the above formula, is the derivative of the Lyapunov energy function F3.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] First, by recursively constructing the Lyapunov function of the closed-loop system, the asymptotic stability of the LCL-type photovoltaic grid-connected inverter system is ensured, and the structuring of the controller design is realized.

[0044] Second, since the sliding mode controller is first used to design the backstepping sliding mode system control law, and then the mapping adaptive algorithm is combined with the backstepping sliding mode system control law to design the adaptive backstepping sliding mode control law, the Lyapunov stability of the LCL-type photovoltaic grid-connected inverter system is ensured by the backstepping method. On this basis, the sliding mode control is used to improve the dynamic performance and robustness of the LCL-type photovoltaic grid-connected inverter system, enabling the system to have good dynamic characteristics and improving the anti-interference ability of the system. In particular, the switching gain in the sliding mode reaching law is obtained through the mapping adaptive law, further improving the self-adaptability of the LCL-type photovoltaic grid-connected inverter system.

[0045] In summary, compared with the prior art, the present invention can not only ensure the global stability of the LCL-type photovoltaic grid-connected inverter system, but also has good robustness against the uncertain changes caused by the system model parameters and external disturbances, and improves the tracking accuracy of the grid-connected current. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0047] Figure 1 The mapping adaptive backstepping sliding mode control block diagram based on state exact linearization of the present invention;

[0048] Figure 2 Equivalent mathematical model diagram of the LCL-type photovoltaic grid-connected inverter of the present invention;

[0049] Figure 3 Block diagram of the existing common technical control method of the LCL-type photovoltaic grid-connected inverter;

[0050] Figure 4 Diagram of the grid-connected photovoltaic power generation system applied in the present invention;

[0051] Figure 5 Main circuit diagram of the LCL-type photovoltaic grid-connected inverter applied in the present invention;

[0052] Figure 6 Dynamic experimental waveforms of the grid-connected current of the three-phase grid-connected inverter of the present invention;

[0053] Figure 7 Total harmonic distortion (THD) diagram of the grid-connected current of phase A of the present invention. Detailed implementation manners

[0054] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0055] The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter provided by the present invention includes the following steps:

[0056] S1. Build an LCL-type photovoltaic grid-connected inverter system. The grid-connected photovoltaic power generation system adopted is as Figure 4 shown, and the LCL-type photovoltaic grid-connected inverter adopted is as Figure 5 shown. PV is a solar photovoltaic panel, L is a large current-stabilizing inductor, S1-S6 are three-phase full-bridge inverter switching tubes, L1 is the output inductor on the inverter side, L2 is the grid-side filter inductor, and C is a filter capacitor;

[0057] S2. Determine the state equation of the grid-connected inverter according to the LCL-type photovoltaic grid-connected inverter;

[0058] Specifically, as the equivalent mathematical model of the LCL-type photovoltaic grid-connected inverter shown in Figure 2 , where G c (s) is a current controller, K PWM is the equivalent transfer function of the inverter, generally set to 1, K is the active damping coefficient, and H is the grid-connected current feedback coefficient;

[0059] The state variables of the grid-connected inverter are selected as follows: i1 is the current on the inverter side, and u c is the voltage of the filter capacitor, and i g is the grid-connected current, and u g is the grid-connected voltage;

[0060] According to Kirchhoff's voltage law and current law, the state equation of the LCL is obtained as follows:

[0061]

[0062] For a single-input single-output system, the affine nonlinear model of the system is

[0063]

[0064] Therefore, the state equation of the LCL grid-connected inverter is rewritten as an affine nonlinear model as follows:

[0065]

[0066] According to the differential geometry theory, the first-order Lie derivative and the second-order Lie derivative are obtained for the grid-connected inverter system:

[0067]

[0068] In the above formula, ad f g(x) is the first-order Lie derivative, is the second-order Lie derivative.

[0069] It can be seen from Equation (6) that the rank of the matrix G(x) is 3, indicating that G(x) is full rank and satisfies the feedback exact linearization condition.

[0070] Calculate the relative degree of the output function:

[0071]

[0072] In the above formula, t is the time variable, is the partial derivative of the output function;

[0073] Perform a linear transformation on Equation (7):

[0074]

[0075] In the above formula, z is the variable in the Z space, and z1, z2, and z3 are the state variables in the Z space;

[0076] Therefore, the state equation of the grid-connected inverter is represented by the Brunovsky canonical form of the single-phase grid-connected inverter in the z space:

[0077]

[0078] In the above formula, z1, z2, and z3 are state variables in the Z space, y is the output variable, v is the control input in the Z space, and is the first derivative of the state variable in the Z space.

[0079] S3. According to the state equation of the grid-connected inverter, the standard state equation of exact linearization is obtained, as Figure 1 shown, specifically including:

[0080] The nonlinear control law in the X space is calculated according to the state equation of the grid-connected inverter formula (9) as:

[0081]

[0082] The state variables in the X space are: The input quantity is the duty cycle u, U in is the input DC power supply, L1 is the output inductor on the inverter side, L2 is the filter inductor on the grid side, C is the filter capacitor, R L is the load, v is the control input in the Z space, i1 is the current on the inverter side, u c is the voltage of the filter capacitor, i g is the grid-connected current;

[0083] Due to reasons such as aging, the parameters of the filter inductor and filter capacitor in the filter circuit will change slightly, and the load will also change over time. Considering the uncertain changes caused by the error between the actual value and the true value of the filter parameters, on the basis of the refined model represented by formula (9), adding parameter changes and internal disturbances, formula (9) is rewritten as:

[0084]

[0085] In actual control, the current on the inverter side, the grid-connected current, and the grid voltage are detected by Hall sensors. Among them, the grid-connected inverter will be affected by various factors, and the main interference comes from the uncertainty of the LCL filter parameters and external interference. Considering the above factors, design it to meet the strict parameter form, and rewrite formula (11) as the following form:

[0086]

[0087] In the above formula, Δ1, Δ2, and Δ3 are uncertainty parameters caused by the error between the actual value and the true value of the LCL filter parameters, and d(t) is the external disturbance, mainly caused by the instability of the DC side voltage.

[0088] Define the function of system parameter uncertainty and external disturbance as:

[0089]

[0090] Substituting Equation (13) into Equation (12), the exact linearized standard state equation is obtained as follows:

[0091]

[0092] In the above equation, is the first derivative of the state variable in the Z space, is the total disturbance.

[0093] S4. According to the exact linearized standard state equation, a sliding mode controller for the LCL-type photovoltaic grid-connected inverter based on the Lyapunov stability theorem is designed using the backstepping method. Then, the control law of the backstepping sliding mode system is designed using the sliding mode controller, as Figure 1 shown, specifically including:

[0094] S41. Before performing the backstepping method, it is necessary to define the tracking error. At the same time, for the exact linearized model, the control objective of the exact linearized model is to control the state variable z1 to track its reference value z d , and according to the backstepping principle, the tracking error e1 is defined as the difference between z1 and z d :

[0095]

[0096] S42. Set the Lyapunov function F1:

[0097]

[0098] Select the intermediate virtual control quantity e2:

[0099]

[0100] where k1 > 0,

[0101] Substituting Equation (18) into Equation (17) gives:

[0102]

[0103] S43. Set the Lyapunov function F2:

[0104]

[0105] Substituting Equation (22) into Equation (21) gives:

[0106]

[0107] Select the intermediate virtual control quantity as e3:

[0108]

[0109] In the above formula, k2 > 0,

[0110] Substituting Equation (24) into Equation (23) gives:

[0111]

[0112] S44. Set the Lyapunov function F3:

[0113]

[0114] According to Equation (26) and Equation (27), we get:

[0115]

[0116] where e2 and e3 are virtual control variables, and e1 is the tracking error;

[0117] S45. Selection of the sliding mode reaching law: and ε > 0, c > 0, where is the sliding mode reaching law, s is the sliding mode surface, c is the sliding mode surface coefficient, and ε is the switching gain of the sliding mode surface;

[0118] The control law of the backstepping sliding mode system is:

[0119]

[0120] S46. Design the adaptive backstepping sliding mode control law by combining the mapping adaptive algorithm with the backstepping sliding mode system control law, as Figure 1 shown;

[0121] Specifically, there are still uncertain factors in the control law Therefore, it is difficult to judge the stability of the system. According to the principle of the grid-connected inverter, the fluctuations of the inductor parameters and capacitor parameters are limited within one cycle. Therefore, the total disturbance Although it is an uncertain factor, it is bounded. Therefore, let K be the maximum value of the total disturbance range. The control parameter ε ≥ K to ensure that the derivative of the Lyapunov energy function F3 ≤ 0, then the sliding mode controller is stable, otherwise it is unstable;

[0122] The derivative of the Lyapunov energy function F3 ≤ 0 is expressed as:

[0123]

[0124] If the switching gain ε is selected in a conservative way to ensure the stability of the system, a severe chattering phenomenon will occur. Therefore, an adaptive algorithm is used to update the switching gain in real time, effectively solving the problem of the switching gain, that is, selecting the switching gain ε for mapping adaptive algorithm calculation,

[0125]

[0126] where λ > 0. According to the sliding mode reaching law, the judgment for satisfying the reachability condition is as follows:

[0127]

[0128] Therefore, in order to prevent from being too large, resulting in an overly large control input signal or the situation of , it is necessary to design an adaptive law to make the estimated value of the switching gain min , max within the range:

[0129]

[0130] When is greater than or equal to the maximum value ε max , if there is a tendency to continue increasing, that is, , then the value of remains unchanged. When is less than or equal to the minimum value ε min , if there is a tendency to continue decreasing, that is, , then the value of remains unchanged.

[0131] Adopt the mapping adaptive algorithm to ensure that the derivative of the Lyapunov energy function F3 ≤ 0;

[0132] S47. Verify the stability of the controller using the Lyapunov function.

[0133] According to the principle of the grid-connected inverter, the fluctuations of the inductor parameters and capacitor parameters are limited within one cycle. Therefore, is bounded. Let The control parameter ε ≥ K, then it is ensured that:

[0134]

[0135] For the overall block diagram of the implementation of the mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter of the present invention, as shown in Figure 1As shown, the acquisition module includes a current signal acquisition module and a voltage signal acquisition module. The inverter-side current, grid-connected current, and capacitor current information are acquired through Hall current sensors, and the filter capacitor voltage and grid connection point voltage information are acquired through Hall voltage sensors. Then, the state equation is accurately linearized, and the backstepping method is adopted to ensure the Lyapunov stability of the system. On this basis, sliding mode control is used to improve the dynamic performance and robustness of the LCL-type photovoltaic grid-connected inverter system. Among them, the switching gain in the sliding mode reaching law is obtained through the mapping adaptive law, which improves the self-adaptability of the LCL-type photovoltaic grid-connected inverter system.

[0136] The embodiments of the mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter of the present invention will be described in detail. Figure 6 It is a dynamic experimental diagram for load switching at the zero-crossing moment. In the experiment of switching from full load of 20 A to half load of 10 A, at t = 0.50 s, the system only takes about 20 ms to reach stability, indicating that the system has fast dynamic performance. Figure 7 It is the experimental result of the total harmonic content analysis of the grid-connected current. Under the adaptive backstepping sliding mode strategy, the total harmonic distortion rate of the grid-connected current is 3.4%, meeting the grid connection standard requirement of less than 5%. It can be seen that under the control method of the present invention, the system with an LCL-type photovoltaic grid-connected inverter has good robustness and power quality.

[0137] In summary, the mapping adaptive backstepping sliding mode control method for an LCL-type photovoltaic grid-connected inverter of the present invention has a good resonance suppression effect. The results show that the proposed mapping adaptive backstepping sliding mode strategy has fast dynamic performance and strong robustness.

[0138] The above-disclosed are only the specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or deformations, which should all be covered within the protection scope of the present invention.

Claims

1. Mapping adaptive backstepping sliding mode control method for LCL type photovoltaic grid-connected inverter, characterized in that, It includes the following steps: S1. Build an LCL-type photovoltaic grid-connected inverter system; S2. Determine the state equation of the grid-connected inverter according to the LCL-type photovoltaic grid-connected inverter; S3. Obtain the accurately linearized standard state equation through the state equation of the grid-connected inverter; S4. According to the accurately linearized standard state equation, design a sliding mode controller for the LCL-type photovoltaic grid-connected inverter based on the Lyapunov stability theorem by using the backstepping method, and then design the control law of the backstepping sliding mode system based on the sliding mode controller; S5. Design an adaptive backstepping sliding mode control law by combining the mapping adaptive algorithm with the control law of the backstepping sliding mode system; The design of the adaptive backstepping sliding mode control law through the mapping adaptive algorithm includes the selection of the sliding mode reaching law: where is the sliding mode reaching law, s is the sliding mode surface, c is the sliding mode surface coefficient, ε is the switching gain of the sliding mode surface, and the switching gain ε is selected for the mapping adaptive algorithm calculation, which specifically includes: The estimated value of the switching gain ε is made to vary within [ε , ε min , ε max by the design of the adaptation law. When , where λ is a coefficient, When is greater than or equal to the maximum value ε max and has a tendency to continue increasing, i.e., then the value taken is unchanged. When is less than or equal to the minimum value ε min and has a tendency to continue decreasing, i.e., then the value taken is unchanged. That is, the design using the adaptive law ensures that the estimated value of the switching gain varies within the range of [ε min , ε max .

2. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 1, wherein: It also includes verifying the stability of the controller by using the Lyapunov function.

3. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 1, characterized in that, The state equation of the grid-connected inverter is represented by the Brunovsky canonical form of the grid-connected inverter in the Z space: In the above formula, z1, z2, and z3 are state variables in the Z space, y is the output variable, and v is the control input in the Z space. is the first derivative of the state variable in the Z space.

4. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 3, wherein Obtaining the accurately linearized standard state equation according to the state equation of the grid-connected inverter specifically includes: The nonlinear control law in the X space calculated according to the state equation of the grid-connected inverter is: In the above formula, the state variables in the X space are: The input quantity is the duty cycle u, and U in is the DC input power supply, L1 is the output inductor on the inverter side, L2 is the filter inductor on the grid side, C is the filter capacitor, and R L is the load, v is the control input in the Z space, i1 is the current on the inverter side, and u c is the voltage of the filter capacitor, and i g is the grid-connected current; Considering the uncertain variation caused by the error between the actual value and the true value of the filter parameters, rewrite the nonlinear control law equation in the X space into the accurately linearized standard state equation, and the accurately linearized standard state equation is: In the above formula, is the first derivative of the state variable in the Z space, is the total disturbance.

5. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 4, characterized in that, According to the accurately linearized standard state equation, design a sliding mode controller for the LCL-type photovoltaic grid-connected inverter based on the Lyapunov stability theorem by using the backstepping method, and then design the control law of the backstepping sliding mode system based on the sliding mode controller, specifically including: The control objective of the exact linearization model is to control the state variable z1 to track its reference value z d , according to the backstepping principle, the tracking error e1 is defined as the difference between z1 and z d : Set the Lyapunov energy function F1: Set the Lyapunov energy function F2: e2 is the intermediate virtual control quantity; Set the Lyapunov energy function F3: e3 is the intermediate virtual control quantity; The control law of the backstepping sliding mode system is: where k1 and k2 are the coefficients of the Lyapunov energy function.

6. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 5, characterized in that, Verifying the stability of the sliding mode controller by using the Lyapunov function specifically includes: According to the principle of the LCL-type photovoltaic grid-connected inverter, the fluctuations of the inductor parameters and capacitor parameters are limited within a cycle. Therefore, the total disturbance is an uncertain factor but bounded. Let K be the maximum value of the total disturbance range. When the control parameter ε ≥ K and the derivative of the Lyapunov energy function F3 ≤ 0, the sliding mode controller is stable; otherwise, it is unstable.

7. The mapping adaptive backstepping sliding mode control method for the LCL-type photovoltaic grid-connected inverter according to claim 6, wherein The derivative of the Lyapunov energy function F3 ≤ 0 is expressed as: In the above formula, is the derivative of the Lyapunov energy function F3.

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