Complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional-integral observer

Abstract

The invention discloses a grid-connected inverter complementary sliding mode control method based on a cascade generalized proportional-integral observer, and the method comprises the steps: firstly building a mathematical model of a grid-connected inverter, and enabling the mathematical model to be used for the design of a controller; and a cascade generalized proportional integral observer is introduced to estimate the lumped disturbance of the hyper-local model so as to improve the anti-disturbance capability and the noise suppression capability of the system. By introducing the complementary sliding mode controller, compared with a traditional sliding mode, the position tracking error is reduced by half. By introducing the improved reaching law, a large reaching speed can be kept when the system state is far away from the sliding mode surface, and the sliding mode reaching speed is weakened when the system state approaches the sliding mode surface, so that the chattering phenomenon of the sliding mode is reduced. According to the control method, the coupling influence of the d axis and the q axis can be obviously inhibited, the harmonic content of the three-phase current is reduced, and stable operation of the grid-connected inverter is facilitated.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular relates to a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer. Background Art

[0002] Since the beginning of the new century, the supply of coal and oil energy has faced an unprecedented crisis. Therefore, vigorously developing renewable energy is an inevitable requirement for the development of human society and the protection of the ecological environment. Encouraged by government policies, the proportion of social capital invested in wind power generation technology and photovoltaic power generation technology is increasing. This type of renewable energy is converted into direct current by power generation equipment, and then converted into alternating current by grid-connected inverters and connected to the large power grid. Therefore, the control method of the grid-connected inverter plays a vital role in the efficient operation of the power grid.

[0003] There are coupling phenomena and nonlinear characteristics in the grid-connected inverter, which contains a large number of harmonic components, threatening the safe operation of the power grid. In order to reduce the harmonic content in the power grid, while adding filters, the use of advanced control strategies can also effectively reduce the harmonic content of the grid-connected current. Therefore, the improvement of the control strategy of the grid-connected inverter has important engineering practical significance.

[0004] With the continuous improvement of modern control theory, the control algorithm of grid-connected inverters is also constantly updated. PI control is controlled by two variables, proportional and integral. Although the implementation method is simple, there will be a certain static error in the tracking of AC signals by PI control. The principle of sliding mode variable structure control is to regularly adjust the current state of the system to run on the set sliding surface. Although it has the advantages of fast response speed and easy algorithm implementation, it has high requirements on the actual value of parameters. With the large-scale investment in new energy, traditional control strategies have shown certain deficiencies in decoupling ability, anti-interference performance and transient response. It is very necessary to design a control strategy with stronger control ability and wide applicability. Summary of the invention

[0005] The purpose of the present invention is to provide a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer, which enhances the anti-disturbance performance of the system and reduces the tracking error of the current reference value.

[0006] The technical solution adopted by the present invention is a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional-integral observer, which is specifically implemented according to the following steps: Step 1: Construct an equivalent mathematical model of the grid-connected inverter; Step 2: Obtain the state space equation of the equivalent object of the grid-connected inverter according to the equivalent mathematical model constructed in step 1; Step 3: Design a cascaded generalized proportional-integral observer; Step 4: Design a sliding mode controller and obtain the control law of the system; Step 5: Obtain the control output through the sliding mode controller constructed in step 4, use sinusoidal pulse width modulation (SPWM) to get the duty cycle, and apply the duty cycle to the control of the grid-connected inverter switch tube to achieve closed-loop control of the system.

[0007] The present invention is also characterized in that: Step 1 is as follows: Under the condition of balanced three-phase voltage of the power grid, according to Kirchhoff's law, the grid-connected inverter abc The variable relationship in the coordinate system is: (1) In formula (1), u a , u b , u c For the inverter side abc Three-phase voltage, i La , i Lb , i Lc The current flowing through the inductor abc Three-phase current, L , C They are the inductor and capacitor filter parameters respectively. R is the parasitic parameter of the filter inductor, u ga , u gb , u gc For AC power grid abc Three-phase voltage; s j is the switching function of the on-off state of each bridge arm switch tube in the grid-connected inverter, j =a,b,c, its specific meaning is: (2) The mathematical model of the AC side of the converter in the dq coordinate system is obtained by transforming equation (1) into: (3) In formula (3), ω is the grid voltage angular frequency, u d , u q They represent the components of the AC voltage on the d and q axes respectively.i Ld , i Lq They represent the components of the inductor current on the d and q axes respectively, u dr = s d u dc , u qr = s q u dc , s d , s q They are the d-axis and q-axis switching functions respectively.

[0008] Step 2 is specifically as follows: On the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector. According to the instantaneous power theory, the power equation is obtained as follows: (4) In formula (4), P ref , Q ref are the reference values ​​of active power and reactive power respectively. i dref , i qref They are the current reference values ​​of the set active power and reactive power respectively; The current reference values ​​of active power and reactive power are obtained from formula (4): (5) The system's internal and external disturbances and parameter perturbations are uniformly expressed as lumped disturbances, and combined with formula (2), we get: (6) In formula (6), b d , b q are the d-axis and q-axis control quantity gains respectively, f d , f q are the equivalent d-axis and q-axis lumped disturbances, respectively. The lumped disturbances include the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The expressions of the d-axis and q-axis lumped disturbances are: (7) Let the state variable x d1 =i Ld , x d2 = f d , x q1 = i Lq , x q2 = f q , then formula (6) can be expressed in the following form: (8) In order to further improve the observation accuracy, the lumped disturbance is expanded, and the state space model of equation (8) is reconstructed as: (9).

[0009] Step 3: Designing a cascaded generalized proportional integral observer includes designing a first-level generalized proportional integral observer and a second-level generalized proportional integral observer. Specifically, the first-level generalized proportional integral observer is designed as follows: definition z d11 , z d12 , z d13 , z q11 , z q12 , z q13 They are x d1 , x d2 , , x q1 , x q2 , The observation value of , according to formula (9), the form of the first-level generalized proportional integral observer is designed as: (10) In formula (10), β 11 , β 12 , β 13 is the first-order observer gain of the d-axis; h 11 , h 12 , h 13 is the first-order observer gain of the q-axis; The second-level generalized proportional integral observer is designed as follows: From equation (10), we know that the estimated value of the total disturbance is subject to the current error e d1 , e q1 The influence of , resulting in the generation of estimation error, in order to further estimate the disturbance error, the first-level estimated disturbance is taken as a known part, and the design of the second-level generalized proportional integral observer is in the form of: (11) In formula (11), β 21 , β 22 , β 23 is the gain of the d-axis of the second-level observer; h 21 , h 22 , h 23 is the gain of the q-axis of the second-level observer; z d21 , z d22 , z d23 is the observed value of the d-axis of the second-level observer; z q21 , z q22 , z q23 is the observed value of the q-axis of the second-level observer, fal ( e , α i , δ ) is a nonlinear function.

[0010] Nonlinear functions fal ( e , α i , δ ) is: (12) In formula (12), fal ( e , α i , δ ) is a power function, α i is the exponential power, δ represents the linear interval.

[0011] Step 4 is as follows: Let the d and q axis grid side currents bei d , i q Deviation from the grid-side current reference value e d , e q for: (13) In formula (13), i dref for i d The reference value of i qref for i q Reference value of Definition of generalized sliding surface s dg , s qg for: (14) In formula (14), λ 1 , λ 2 is the gain of the sliding surface, and the design is s dg , s qg Orthogonal complementary sliding surfaces s dc , s qc for: (15) The total sliding surface of the d and q axes is s d , s q It is expressed as: (16) From formula (15), the relationship between the sliding surfaces is: (17) In order to make the system reach a stable state, the Lyapunov function is selected V d , V q for: (18) Derivative of formula (18) yields: (19) The equivalent control law of d and q axes is obtained from equation (19): (20) The double power reaching law is adopted, and its specific form is: (twenty one) In formula (21), k 1 , k 2 , k 3 , k 4 is the parameter of the double power reaching law, m 1 and m 2 All are greater than 1, n 1 and n 2 Both are greater than 0 and less than 1; Combining the equivalent control law of formula (20) and the switching control law of formula (21), the comprehensive control law of the grid-connected inverter is obtained as follows: (twenty two).

[0012] In formula (14), λ 1 , λ 2 ≥0.

[0013] The beneficial effects of the present invention are: The complementary sliding mode control method of the grid-connected inverter based on the cascaded generalized proportional integral observer is introduced to shorten the position tracking error of the sliding mode. The introduced double power reaching law can adaptively adjust the gain size in the sliding mode motion. The introduction of the cascaded generalized proportional integral observer can effectively suppress the influence caused by external disturbances. Finally, the combination of the cascaded generalized proportional integral observer and the complementary sliding mode makes the system have higher accuracy and better robustness, and has better dynamic response capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the topological structure diagram of the grid-connected inverter; Figure 2 It is a control block diagram of a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional-integral observer according to the present invention; Figure 3 It is a control diagram of the complementary sliding mode control method of the grid-connected inverter based on the cascaded generalized proportional integral observer of the present invention; Figure 4 is the load power consumption demand diagram; Figure 5This is the transient response diagram of the three-phase current under PI control when the active power changes suddenly; Figure 6 It is a transient response diagram of three-phase current controlled by the control method of the present invention when active power suddenly changes; Figure 7 It is the transient response diagram of d and q axis current under PI control; Figure 8 is a transient response diagram of d and q axis currents controlled by the control method of the present invention; Fig. 9 It is the transient response diagram of three-phase current under PI control; Fig.10 is a transient response diagram of three-phase current controlled by the control method of the present invention; Fig.11 It is a harmonic analysis diagram of grid-connected current controlled by PI control method.

[0015] Fig.12 It is a harmonic analysis diagram of the grid-connected current controlled by the control method of the present invention. DETAILED DESCRIPTION

[0016] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Example 1 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional-integral observer, which is specifically implemented according to the following steps: Step 1: Construct an equivalent mathematical model of the grid-connected inverter; Step 2: Obtain the spatial state equation of the equivalent object of the grid-connected inverter according to the equivalent mathematical model constructed in step 1; Step 3: Design a cascaded generalized proportional-integral observer; Step 4: Design a sliding mode controller and obtain the control law of the system; Step 5: Obtain the control output through the sliding mode controller constructed in step 4, use SPWM modulation to get the duty cycle, and apply the duty cycle to the control of the grid-connected inverter switch tube to achieve closed-loop control.

[0018] Example 2 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer. Based on Embodiment 1, step 1 is specifically as follows: the circuit structure of the grid-connected inverter is as follows: Figure 1 As shown, the DC side voltage is provided by the DC power supply, and the inverter is controlled to output a certain power to supply the AC load. In this figure, u in is the voltage across the DC voltage source, C dc is the DC side stabilizing capacitor,i o Indicates the current output on the DC side, i a , i b , i c is the three-phase current on the grid side. Under the condition of balanced three-phase voltage of the grid, according to Kirchhoff's law, the grid-connected inverter is abc The variable relationship in the coordinate system is: (1) In formula (1), u a , u b , u c For the inverter side abc Three-phase voltage, i La , i Lb , i Lc The current flowing through the inductor abc Three-phase current, L , C They are the inductor and capacitor filter parameters respectively. R is the parasitic parameter of the filter inductor, u ga , u gb , u gc For AC power grid abc Three-phase voltage; s j is the switching function of the on-off state of each bridge arm switch tube in the grid-connected inverter, j =a,b,c, its specific meaning is: (2) The mathematical model of the AC side of the converter in the dq coordinate system is obtained by transforming equation (1) into: (3) In formula (3), ω is the grid voltage angular frequency, u d , u q They represent the components of the AC voltage on the d and q axes respectively. i Ld , i Lq They represent the components of the inductor current on the d and q axes respectively, u dr =s d u dc , u qr = s q u dc , s d , s q They are the d-axis and q-axis switching functions respectively.

[0019] Example 3 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer. On the basis of Embodiments 1-2, step 2 is specifically, on the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector, and according to the instantaneous power theory, the power equation is obtained as follows: (4) In formula (4), P ref , Q ref are the reference values ​​of active power and reactive power respectively. i dref , i qref They are the current reference values ​​of the set active power and reactive power respectively; The current reference values ​​of active power and reactive power are obtained from formula (4): (5) The system's internal and external disturbances and parameter perturbations are uniformly expressed as lumped disturbances, and combined with formula (3), we get: (6) In formula (6), b d , b q are the d-axis and q-axis control quantity gains respectively, f d , f q are the equivalent d-axis and q-axis lumped disturbances, respectively. The lumped disturbances include the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The expressions of the d-axis and q-axis lumped disturbances are: (7) Let the state variable x d1 = i Ld , x d2= f d , x q1 = i Lq , x q2 = f q , then formula (6) can be expressed in the following form: (8) In order to further improve the observation accuracy, the lumped disturbance is expanded, and the state space model of equation (8) is reconstructed as: (9).

[0020] Example 4 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional-integral observer. On the basis of Embodiments 1-3, step 3 of designing a cascaded generalized proportional-integral observer includes designing a first-level generalized proportional-integral observer and a second-level generalized proportional-integral observer. The design of the first-level generalized proportional-integral observer is specifically as follows: definition z d11 , z d12 , z d13 , z q11 , z q12 , z q13 They are x d1 , x d2 , , x q1 , x q2 , The observation value of , according to formula (9), the form of the first-level generalized proportional integral observer is designed as: (10) In formula (10), β 11 , β 12 , β 13 is the first-order observer gain of the d-axis; h 11 , h 12 , h 13 is the first-order observer gain of the q-axis.

[0021] Example 5 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer. On the basis of Embodiments 1-4, the second-level generalized proportional integral observer is designed as follows: From equation (10), it is known that the estimated value of the total disturbance is affected by the current error e d1 , e q1 The influence of , resulting in the generation of estimation error, in order to further estimate the disturbance error, the first-level estimated disturbance is taken as a known part, and the design of the second-level generalized proportional integral observer is in the form of: (11) In formula (11), β 21 , β 22 , β 23 is the gain of the d-axis of the second-level observer; h 21 , h 22 , h 23 is the gain of the q-axis of the second-level observer; z d21 , z d22 , z d23 is the observed value of the d-axis of the second-level observer; z q21 , z q22 , z q23 is the observed value of the q-axis of the second-level observer, and the nonlinear function fal ( e , α i , δ ) is: (12) In formula (12), fal ( e , α i , δ ) is a power function, α i is the exponential power, δ represents the linear interval.

[0022] Example 6 This embodiment provides a complementary sliding mode control method for a grid-connected inverter based on a cascaded generalized proportional integral observer. On the basis of Embodiment 1-2, step 4 is specifically as follows: Let the d and q axis grid side currents be i d , i q Deviation from the grid-side current reference value e d , e q for: (13) In formula (13), i dref for i d The reference value of i qref for i q Reference value of Definition of generalized sliding surface s dg , s qg for: (14) In formula (14), λ 1 , λ 2 ≥0, λ 1 , λ 2 is the gain of the sliding surface, and the design is s dg , s qg Orthogonal complementary sliding surfaces s dc , s qc for: (15) The total sliding surface of the d and q axes is s d , s q It is expressed as: (16) From formula (15), the relationship between the sliding surfaces is: (17) In order to make the system reach a stable state, the Lyapunov function is selected V d , Vq for: (18) Derivative of formula (18) yields: (19) The equivalent control law of d and q axes is obtained from equation (19): (20) In the complementary sliding surface arrival stage, in order to weaken the system chattering and improve the error convergence speed, the double power reaching law is adopted, and its specific form is: (twenty one) In formula (21), k 1 , k 2 , k 3 , k 4 is the parameter of the double power reaching law, m 1 and m 2 All are greater than 1, n 1 and n 2 Both are greater than 0 and less than 1; Combining the equivalent control law of formula (20) and the switching control law of formula (21), the comprehensive control law of the grid-connected inverter is obtained as follows: (twenty two).

[0023] like Figure 3 The control diagram of the complementary sliding mode control method of the grid-connected inverter based on the cascaded generalized proportional integral observer of the present invention is shown. The control method of the present invention has the following advantages: 1) The control method of the present invention enables the grid-connected inverter to realize power backup, and can flexibly control the active power and reactive power, so that the grid-connected inverter can take into account PQ Control grid-connected advantages.

[0024] 2) The control method of the present invention improves the traditional anti-disturbance control and introduces a cascade structure to enhance the anti-disturbance performance of the system. This method improves the estimation accuracy of disturbances. Adding nonlinear functions to the cascade structure can improve the efficiency of the observer. The linear observer of the front stage is used to observe large disturbances, and the nonlinear observer of the back stage is used to estimate small disturbances and disturbance residuals. At the same time, the estimation of high-order disturbances is introduced in the cascade, which can estimate various types of time-varying disturbances, thereby improving the tracking accuracy and anti-disturbance performance of the grid-connected inverter system.

[0025] 3) The controller of the present invention adopts complementary sliding mode control, and its sliding surface adopts a combination of generalized sliding surface and complementary sliding surface, so that the tracking error slides along the intersection of the two sliding surfaces toward the area near the zero point and reaches the vicinity of the sliding surface within a finite time. Compared with the traditional sliding mode, the position tracking error of the complementary sliding mode is halved. Therefore, the convergence of the tracking error of the complementary sliding mode system within a finite time can be guaranteed.

[0026] 4) The invention introduces the double power reaching law in the complementary sliding mode control, which can greatly reduce the chattering when reaching the sliding mode surface. When the system state is far away from the sliding mode, the approaching speed will remain large. When the system state is close to the sliding mode, the approaching speed will continue to slow down, realizing the smooth transition of the sliding mode. And the larger the initial error, the more obvious the approaching speed advantage of the double power reaching law.

[0027] Experimental analysis In order to verify the effectiveness of the complementary sliding mode control method of the grid-connected inverter based on the cascaded generalized proportional-integral observer of the present invention, in the grid-connected inverter model built in the Matlab / Simulink platform, Figure 4 As shown, in order to compare the dynamic performance of the three-phase current on the inverter output side when the load suddenly increases or decreases, a power command of -35kW is given to the grid-connected inverter at 0.25s, and the grid-connected inverter suddenly changes from the inverter state to the rectifier state; a power command of 50kW is given to the grid-connected inverter at 0.3s, and the grid-connected inverter suddenly changes from the rectifier state to the inverter state, simulating the random switching of the load.

[0028] Under the two control modes, when the active power suddenly changes, the output of the stable operation 50kW drops suddenly to -35kW at 0.25s, and the corresponding three-phase current amplitude drops suddenly from 107A to 75A, and the grid-connected inverter changes from the inverter state to the rectifier state; at 0.3s, it suddenly increases from -35kW to 50kW, and the corresponding three-phase current amplitude increases suddenly from 75A to 107A, and the grid-connected inverter changes from the rectifier state to the inverter state, resulting in the dynamic response of the three-phase current output on the AC side of the three-phase inverter. Figure 5 As shown in the figure, under the traditional PI control, the response time of the three-phase current on the grid side is 17ms at 0.25s, and the current change amplitude at the moment of jump is 220A; the response time of the three-phase current on the grid side is 16ms at 0.3s. Figure 6 As shown in the figure, under the control of the control method of the present invention, the response time of the three-phase current on the grid side is 9ms at 0.25s, and the current change amplitude at the moment of jump is 63A; the response time of the three-phase current on the grid side is 15ms at 0.3s. By comparison, it can be seen that the control method of the present invention greatly reduces the transient time and the amplitude of the three-phase current jump, avoids the electrical equipment from being affected by overcurrent, and improves the operational stability of the power system.

[0029] In order to verify the effectiveness of the control method of the present invention, a simulation circuit is built in a hardware-in-the-loop (HIL) experimental platform, and a comparative analysis is performed with the traditional PI control strategy. It is defined that the power is positive when the voltage and current directions are consistent. The simulation parameter settings are shown in Table 1.

[0030] Table 1 Circuit parameters

[0031] The power response speed of the grid-connected inverter is one of the important indicators to measure the quality of the converter system. From formula (5), we can see that the power response speed is related to the current i d The response speed is consistent. When the grid-connected inverter output power suddenly changes from -35kW to 50kW, Figure 7 It can be seen that the traditional PI control takes 22.5ms to reach the given power value, and there is an obvious coupling phenomenon in the q-axis current, with a current overshoot of 62A and a transient transition time of 38ms. Figure 8 It can be seen that the control method of the present invention only takes 18 ms to reach a given power value, and the q-axis current is less affected by the d-axis and q-axis coupling.

[0032] Depend on Fig. 9 It can be seen that when the output active power of the three-phase inverter jumps from -35kW to 50kW, the response time of the three-phase current on the grid side is 33ms under the PI control strategy. Fig.10 It can be seen that under the control method of the present invention, the jump caused by the sudden increase in power makes the transition time of the three-phase current on the AC side 26ms, and the fluctuation of the current value during steady-state operation is smaller than that of PI control.

[0033] In order to verify the influence of the control method of the present invention on the power quality of the output current of the grid-connected inverter, the Fourier analysis of the grid-connected current of the grid-connected inverter with an output active power of 35kW for 10 steady-state cycles was performed in Matlab / Simulink software. Fig.11 The figure shows the harmonic analysis of the grid-connected current of the grid-connected inverter under PI control, and the THD is 4.69%. Fig.12 The figure shows the harmonic analysis of the grid-connected current of the grid-connected inverter under the control of the control method of the present invention, and the THD is 1.18%. Therefore, the control method of the present invention has a certain harmonic suppression capability and improves the quality of grid-connected power.

[0034] In summary, the control method of the present invention effectively solves the problem that when the grid-connected inverter is subjected to external time-varying disturbances in the grid-connected working mode, the three-phase current on the grid-connected side can be quickly restored to a stable state, thereby improving the convergence speed and control accuracy of the grid-connected inverter and effectively improving the power quality of the power grid.

Claims

1. A complementary sliding mode control method for grid-connected inverters based on cascaded generalized proportional-integral observers, characterized in that: Follow the steps below to implement it: Step 1: Construct an equivalent mathematical model of the grid-connected inverter; Step 2: Obtain the spatial state equation of the equivalent object of the grid-connected inverter according to the equivalent mathematical model constructed in step 1; Step 3: Design a cascaded generalized proportional-integral observer; Step 4: Design a sliding mode controller and obtain the control law of the system; Step 5: Obtain the control output through the sliding mode controller constructed in step 4, use sinusoidal pulse width modulation SPWM modulation to obtain the duty cycle, and apply the duty cycle to the control of the grid-connected inverter switch tube to achieve closed-loop control.

2. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 1, characterized in that: The step 1 is specifically as follows: Under the condition of balanced three-phase voltage of the power grid, according to Kirchhoff's law, the grid-connected inverter abc The variable relationship in the coordinate system is: (1) In formula (1), u a , u b , u c For the inverter side abc Three-phase voltage, i La , i Lb , i Lc The current flowing through the inductor abc Three-phase current, L , C They are the inductor and capacitor filter parameters respectively. R is the parasitic parameter of the filter inductor, u ga , u gb , u gc For AC power grid abc Three-phase voltage; s j is the switching function of the on-off state of each bridge arm switch tube in the grid-connected inverter, j =a,b,c, its specific meaning is: (2) The mathematical model of the AC side of the converter in the dq coordinate system is obtained by transforming equation (1) into: (3) In formula (3), ω is the grid voltage angular frequency, u d , u q They represent the components of the AC voltage on the d and q axes respectively. i Ld , i Lq They represent the components of the inductor current on the d and q axes respectively, u dr = s d u dc , u qr = s q u dc , s d , s q They are the d-axis and q-axis switching functions respectively.

3. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 2, characterized in that: The step 2 is specifically as follows: On the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector. According to the instantaneous power theory, the power equation is obtained as follows: (4) In formula (4), P ref , Q ref are the reference values ​​of active power and reactive power respectively. i dref , i qref They are the current reference values ​​of the set active power and reactive power respectively; The current reference values ​​of active power and reactive power are obtained from formula (4): (5) The system's internal and external disturbances and parameter perturbations are uniformly expressed as lumped disturbances, and combined with formula (3), we get: (6) In formula (6), b d , b q are the d-axis and q-axis control quantity gains respectively, f d , f q are the equivalent d-axis and q-axis lumped disturbances, respectively. The lumped disturbances include the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The expressions of the d-axis and q-axis lumped disturbances are: (7) Let the state variable x d1 = i Ld , x d2 = f d , x q1 = i Lq , x q2 = f q , then formula (6) can be expressed in the following form: (8) In order to further improve the observation accuracy, the lumped disturbance is expanded, and the state space model of equation (8) is reconstructed as: (9)。 4. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 3, characterized in that: The step 3 of designing a cascaded generalized proportional integral observer includes designing a first-level generalized proportional integral observer and a second-level generalized proportional integral observer. The design of the first-level generalized proportional integral observer is specifically as follows: definition z d11 , z d12 , z d13 , z q11 , z q12 , z q13 They are x d1 , x d2 , , x q1 , x q2 , The observation value of , according to formula (9), the form of the first-level generalized proportional integral observer is: (10) In formula (10), β 11 , β 12 , β 13 is the first-order observer gain of the d-axis; h 11 , h 12 , h 13 is the first-order observer gain of the q-axis.

5. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 4, characterized in that: The second-level generalized proportional integral observer is designed as follows: From equation (10), we know that the estimated value of the total disturbance is subject to the current error e d1 , e q1 The influence of , resulting in the generation of estimation error, in order to further estimate the disturbance error, the first-level estimated disturbance is taken as a known part, and the design of the second-level generalized proportional integral observer is in the form of: (11) In formula (11), β 21 , β 22 , β 23 is the gain of the d-axis of the second-level observer; h 21 , h 22 , h 23 is the gain of the q-axis of the second-level observer; z d21 , z d22 , z d23 is the observed value of the d-axis of the second-level observer; z q21 , z q22 , z q23 is the observed value of the q-axis of the second-level observer, fal ( e , α i , δ ) is a nonlinear function.

6. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 5, characterized in that: Nonlinear functions fal ( e , α i , δ ) is: (12) In formula (12), fal ( e , α i , δ ) is a power function, α i is the exponential power, δ represents the linear interval.

7. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 5, characterized in that: The step 4 is specifically as follows: Let the d and q axis grid side currents be i d , i q Deviation from the grid-side current reference value e d , e q for: (13) In formula (13), i dref for i d The reference value of i qref for i q Reference value of Definition of generalized sliding surface s dg , s qg for: (14) In formula (14), λ 1, λ 2 is the gain of the sliding surface, and the design is s dg , s qg Orthogonal complementary sliding surfaces s dc , s qc for: (15) The total sliding surface of the d and q axes is s d , s q It is expressed as: (16) From formula (15), the relationship between the sliding surfaces is: (17) In order to make the system reach a stable state, the Lyapunov function is selected V d , V q for: (18) Derivative of formula (18) yields: (19) The equivalent control law of d and q axes is obtained from equation (19): (20) The double power reaching law is adopted, and its specific form is: (21) In formula (21), k 1. k 2. k 3. k 4 is the parameter of the double power reaching law, m 1 and m 2 are both greater than 1, n 1 and n 2 are both greater than 0 and less than 1; Combining the equivalent control law of formula (20) and the switching control law of formula (21), the comprehensive control law of the grid-connected inverter is obtained as follows: (22)。 8. The complementary sliding mode control method for grid-connected inverter based on cascaded generalized proportional integral observer according to claim 7, characterized in that: In the formula (14), λ 1, λ 2≥0.

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