Energy storage converter backstepping sliding mode control method based on cascade generalized proportional-integral observer

Abstract

The invention discloses a backstepping terminal sliding mode control method based on a cascade generalized proportional integral observer. The backstepping terminal sliding mode control method is applied to closed-loop control of an energy storage converter system. Establishing a mathematical model of the energy storage converter system, and estimating and compensating uncertain parameters of the system and uncertain interference of the environment by using an expansion structure added with disturbance; a cascade generalized proportional-integral observer is designed, so that the estimation precision of the observer is effectively improved; a backstepping terminal sliding mode control method is designed, so that the system can approach a balance point more quickly in any state. Through simulation and experiment verification, compared with traditional PI control, the control method has the advantages that the convergence speed and the tracking precision are obviously better, and a set track can be tracked with a smaller error.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronics, and particularly relates to a backstepping sliding mode control method for a energy storage converter based on a cascaded generalized proportional integral observer. Background Art

[0002] Benefiting from outstanding advantages such as high operating efficiency and friendliness to renewable energy access, the energy storage converter (Power Conversion System, PCS) has been widely used globally. The energy storage converter has functions such as AC-DC conversion, frequency modulation, and voltage regulation, and plays a crucial role in new energy fields such as DC microgrids. Therefore, improving the control strategy of the energy storage converter is the key to ensuring the stable operation of the microgrid system.

[0003] The energy storage converter has the functions of energy storage and energy conversion. Due to its low total harmonic distortion effect of voltage and current, it is widely used in occasions with high power quality requirements such as uninterruptible power supplies. In recent years, due to the complex nonlinear structure of the energy storage converter itself, a large number of advanced control strategies have been applied to such systems.

[0004] In terms of control strategies, existing traditional control methods such as PID control, fuzzy control, repetitive control, and deadbeat control have limited suppression effects when dealing with nonlinear systems, which may cause steady-state errors in the control system. In recent years, new control strategies have been continuously proposed. For example, the predictive control method has received extensive attention in the field of power electronics due to its advantages such as fast dynamic response. Summary of the Invention

[0005] The purpose of the present invention is to provide a backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer, which improves the accuracy and convergence speed of system errors.

[0006] The technical solution adopted by the present invention is a backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer, which is specifically implemented according to the following steps: Step 1: Use sensors to obtain three-phase grid voltage and current, and use a phase-locked loop to control the magnitude and phase of the voltage to be consistent with the grid voltage, and obtain the reference grid-connected current in the rotating coordinate system by PQ control; Step 2: Subtract the actual grid-connected current from the reference grid-connected current to obtain a control error, and use a cascaded generalized proportional integral observer to estimate the derivative of the system output value and the total disturbance; Step 3: Reconstruct the state space model and design a cascaded generalized proportional integral observer; Step 4: Design a backstepping terminal sliding mode controller; Step 5: Obtain the control output through the backstepping terminal sliding mode controller constructed in Step 4, use sinusoidal pulse width modulation (SPWM) to obtain the duty cycle, and apply the duty cycle to the control of the energy storage converter switching tubes, thereby achieving closed-loop control.

[0007] The features of the present invention also lie in that Step 1 is specifically as follows: Under the condition of balanced grid voltage, the variable relationship of the energy storage converter in abc the coordinate system is: (1) In Equation (1), u a , u b , u c are abc three-phase voltages, i La , i Lb , i Lc are the abc three-phase currents flowing through the inductor, L , C are the inductor and capacitor filtering parameters respectively, R is the parasitic parameter of the filter inductor, u ga , u gb , u gc are the abc grid voltages, i a , i b , i c are the abc three-phase grid-side currents; After coordinate transformation of Equation (1), the mathematical model of the AC side of the converter in the d-q coordinate system is: (2) In Equation (2), ω is the grid voltage angular frequency, u d , u q respectively represent the components of the AC voltage on the d and q axes, i Ld , i Lq respectively represent the components of the inductor current on the d and q axes, i d , iq respectively represent the components of the grid-side current on the d-axis and q-axis, u dr = s d u dc , u qr = s q u dc , s d 、 s q are the switching functions on the d-axis and q-axis respectively, and the switching function is defined as: (3).

[0008] Step 2 is specifically: Based on the three-phase balance of the grid voltage, taking the d-axis direction of the grid voltage as the direction of the voltage vector, according to the instantaneous power theory, the power equation is obtained as: (4) In formula (4), P ref 、 Q ref are the reference values of the set active power and reactive power respectively, i dref 、 i qref are the current reference values of the set active power and reactive power respectively; The current reference values of the active power and reactive power are obtained from formula (4) as: (5) Unify the internal and external disturbances and parameter perturbations of the system with lumped disturbances, and combine with formula (2) to get: (6) In formula (6), b d 、 b q are the control quantity gains on the d-axis and q-axis respectively, f d 、 f q are the equivalent lumped disturbances on the d-axis and q-axis respectively. The lumped disturbances include the unmodeled part, the coupling part, and the internal and external disturbances of the system. The expressions of the lumped disturbances on the d-axis and q-axis are: (7) Let the state variable x d1 =i Ld , x d2 = f d , x q1 = i Lq , x q2 = f q Then, Equation (6) is expressed in the following form: (8) 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 is specifically as follows: Define z d11 , z d12 , z d13 , z d14 , z q11 , z q12 , z q13 , z q14 are respectively x d1 , x d2 , f d , , x q1 , x q2 , f q , the observed values of, and according to Equation (9), the form of the first - stage generalized proportional - integral observer is designed as: (10) In Equation (10), β 11 , β 12 , β 13 , β 14 are the first - stage observer gains of the d - axis; h 11 , h12 , h 13 , h 14 is the first-stage observer gain for the q-axis; To further estimate the disturbance error, taking the first-stage estimated disturbance as the known part, design the second-stage general proportional-integral observer in the form of: (11) In equation (11), β 21 , β 22 , β 23 , β 24 are the gains of the d-axis of the second-stage observer; h 21 , h 22 , h 23 , h 24 are the gains of the q-axis of the second-stage observer; z d21 , z d22 , z d23 , z d24 are the observed values of the d-axis of the second-stage observer; z q21 , z q22 , z q23 , z q24 are the observed values of the q-axis of the second-stage observer, is a non-linear function.

[0010] Non-linear function The expression of is: (12) In equation (12), 0 < α i < 1, is the exponential power coefficient; δ is a positive constant.

[0011] Step 4 is specifically implemented according to the following steps: Step 4.1: Define the virtual control variable and the error variable, and design the non-singular fast terminal sliding mode surface; Step 4.2: Design the equivalent control law and the switching control law to obtain the comprehensive control law of the energy storage converter on the d- and q-axes.

[0012] Step 4.1 specifically is Let the deviation between the d-axis and q-axis current values after coordinate transformation and the reference values e 1, e 2 be: (13) In formula (13), i dref is i d 's reference value, i qref is i q 's reference value; To meet the system stability requirements, select the Lyapunov function V d , V q as: (14) And take the time derivative of formula (14) to get: (15) Define x d2 = p d , x q2 = p q , and based on the recursive design idea of the backstepping method, define the virtual control variables p d , p q as: (16) In formula (16), l 1, l 2 are the control parameters to be designed respectively; Define the error variable e 3, e 4 as: (17) And take the time derivative of formula (17) to get: (18) In formula (18), , ; According to formula (18), design the d-axis and q-axis non-singular fast terminal sliding mode surfaces s d , s q as: (19) In Equation (19), γ 1. γ 2. γ 3. γ 4 is the gain of the sliding surface and is a positive real number; h 1. h 2. g 1. g Both 1 and 2 are greater than 1 and less than 2, g 1> h 1, g 2> h 2; Step 4.2 is specifically: Taking the time derivative of Equation (19) gives: (20) Based on the equivalent control method, an equivalent control law is designed according to Equation (20) u dreq 、 u qreq as: (21) Since Equation (21) contains the derivative forms of the virtual control variables p d 、 p q To avoid the phenomenon of differential explosion, the following second-order filter is introduced to estimate them: (22) In Equation (22), ε represents p d or p q ; τ 1. τ 2 are the filtering time constants; λ 1. λ 2. ρ 1. ρ 2 are the sliding mode filter constants to be designed; is p d or p q 's filtered value, is or 's estimated value; Furthermore, Equation (21) is re-expressed as: (23) In formula (23), represents the estimated value of, represents the estimated value of; Taking the composite variable-speed reaching law as the switching control law of the sliding mode, the d-axis and q-axis switching control laws are as follows: (24) In formula (24), k 1. k 2. k 3 is the gain of the d-axis reaching law, k 4. k 5. k 6 is the gain of the q-axis reaching law, δ 1. δ 2 is a variable exponential parameter, and the specific representation form is as follows: (25) In formula (25), σ 1. σ 2 are both greater than 1, ε 1. ε 2 are both greater than 0 and less than 1, μ 1. μ 2 are both greater than 0, s d , s q are the sliding mode surfaces; Combining the equivalent control law of formula (23) and the switching control law of formula (24), the comprehensive control laws of the energy storage converter on the d-axis and q-axis are: (26).

[0013] The beneficial effects of the present invention are: The energy storage converter backstepping sliding mode control method based on the cascaded generalized proportional integral observer of the present invention equivalently treats uncertain terms such as d-q axis coupling terms and internal and external disturbances with lumped disturbances, observes and compensates them through a cascaded generalized proportional integral observer, and then designs a backstepping terminal sliding mode control rate as feedback to improve the accuracy and convergence speed of system errors, effectively suppressing the coupling between powers and shortening the transient transition time of grid current. Description of the Drawings

[0014] Figure 1 is the control block diagram of the energy storage converter backstepping sliding mode control method based on the cascaded generalized proportional integral observer of the present invention; Figure 2 is the topological structure diagram of the energy storage converter; Figure 3It is the control schematic diagram of the energy storage converter backstepping sliding mode control method based on the cascaded generalized proportional integral observer of the present invention; Figure 4 It is the transient process diagram of the bus voltage during load switching; Figure 5 It is the harmonic analysis diagram of the grid current under PI control; Figure 6 It is the harmonic analysis diagram of the grid current controlled by the present invention; Figure 7 It is the fluctuation diagram of the DC bus voltage under PI control when the output active power jumps from 20kW to 70kW; Figure 8 It is the fluctuation diagram of the DC bus voltage controlled by the present invention when the output active power jumps from 20kW to 70kW; Figure 9 It is the fluctuation diagram of the DC bus voltage under PI control when the output active power jumps from 70kW to 20kW; Figure 10 It is the fluctuation diagram of the DC bus voltage controlled by the present invention when the output active power jumps from 70kW to 20kW. Detailed implementation manners

[0015] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0016] Example 1 This example provides an energy storage converter backstepping sliding mode control method based on a cascaded generalized proportional integral observer, as Figure 1 shown, and is specifically implemented according to the following steps: Step 1: Use sensors to obtain the three-phase grid voltage and current, and use a phase-locked loop to control the magnitude and phase of the voltage to be consistent with the grid voltage. The PQ control is used to obtain the reference grid-connected current in the rotating coordinate system; Step 2: Subtract the actual grid-connected current from the reference grid-connected current to obtain the control error, and use a cascaded generalized proportional integral observer to estimate the derivative of the system output value and the total disturbance; Step 3: Output the control error, the observed total disturbance, and the derivative of the system output value in the two-phase rotating coordinate system obtained in Step 2 to the backstepping sliding mode controller. After calculation, the reference value of the output voltage of the system in the two-phase rotating coordinate system is obtained; Step 4: Obtain the control output through the sliding mode controller constructed in Step 3, use Sinusoidal Pulse Width Modulation (SPWM) to obtain the duty cycle, and apply the duty cycle to the control of the energy storage converter switching tubes, thereby realizing closed-loop control.

[0017] Example 2 This embodiment provides a backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer. On the basis of Embodiment 1, Step 1 is specifically as follows. The circuit structure of the energy storage converter is as Figure 2 shown. The DC-side voltage is provided by a DC power supply, and a certain power is output by controlling the inverter to supply an AC load. In this figure, u in is the voltage across the DC voltage source, C dc is the DC-side voltage stabilizing capacitor, i o represents the current output on the DC side, i a , i b , i c are the three-phase currents on the grid side; Under the condition of balanced three-phase grid voltages, according to Kirchhoff's law, the variable relationship of the energy storage converter in the abc coordinate system is: (1) In Equation (1), u a , u b , u c are abc the three-phase voltages, i La , i Lb , i Lc are the abc three-phase currents flowing through the inductor, L , C are the inductor and capacitor filtering parameters respectively, R is the parasitic parameter of the filter inductor, u ga , u gb , u gc are the abc AC grid i a , i b , i c are the abc three-phase currents on the grid side; Equation (1) is transformed through coordinate transformation to obtain the mathematical model of the AC side of the converter in the d-q coordinate system as: (2) In Equation (2), ω is the angular frequency of the grid voltage, u d , u q respectively represent the components of the AC voltage on the d-axis and q-axis, i Ld , i Lq respectively represent the components of the inductor current on the d-axis and q-axis, i d , i q respectively represent the components of the grid-side current on the d-axis and q-axis, u dr = s d u dc , u qr = s q u dc , s d , s q are the d-axis and q-axis switching functions respectively, and the switching function is defined as: (3).

[0018] Embodiment 3 This embodiment provides a backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer. On the basis of Embodiments 1-2, 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: (4) In Equation (4), P ref , Q ref are the reference values of the set active power and reactive power respectively, i dref , i qref are the current reference values of the set active power and reactive power respectively; The current reference values of the active power and reactive power are obtained from Equation (4) as: (5) Unify the internal and external disturbances and parameter perturbations of the system with lumped disturbances, and combine with Equation (2) to obtain: (6) In formula (6), b d and b q are the d-axis and q-axis control quantity gains respectively, f d and f q are the lumped disturbances of the d-axis and q-axis after equivalence. The lumped disturbance includes the unmodeled part, the coupling part, and the internal and external disturbances of the system. The expressions of the lumped disturbances of the d-axis and q-axis are: (7) Let the state variables x d1 = i Ld , x d2 = f d , x q1 = i Lq , x q2 = f q , then formula (6) is expressed in the following form: (8) To further improve the observation accuracy, the lumped disturbance is expanded, and the state-space model of formula (8) is reconstructed as: (9).

[0019] Embodiment 4 This embodiment provides a backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer. On the basis of Embodiments 1-3, step 3 is specifically as follows: Define z d11 and z d12 and z d13 and z d14 and z q11 and z q12 and z q13 and z q14 are respectively x d1 and x d2 and f d and andx q1 、 x q2 、 f q 、 The observed values of (10) In formula (10), β 11 、 β 12 、 β 13 、 β 14 are the first - stage observer gains for the d - axis; h 11 、 h 12 、 h 13 、 h 14 are the first - stage observer gains for the q - axis; To further estimate the disturbance error, taking the first - stage estimated disturbance as the known part, the form of the second - stage generalized proportional - integral observer is designed as: (11) In formula (11), β 21 、 β 22 、 β 23 、 β 24 are the gains of the d - axis of the second - stage observer; h 21 、 h 22 、 h 23 、 h 24 are the gains of the q - axis of the second - stage observer; z d21 、 z d22 、 z d23 、 z d24 are the observed values of the d - axis of the second - stage observer; z q21 、 z q22 、 z q23 、 z q24is the observed value of the q-axis of the second-level observer, and the non-linear function has the following expression: (12) In formula (12), 0 < α i < 1 is the exponential power coefficient; δ is a positive constant; α i If the value of i is too small, it will cause high-frequency tremors in the system output. If the value is too large, it will increase the delay degree of the tracking signal.

[0020] Example 5 This example provides a backstepping sliding mode control method for a energy storage converter based on a cascaded generalized proportional-integral observer. On the basis of Examples 1-4, step 4 is specifically implemented according to the following steps: Step 4.1: Define virtual control variables and error variables, and design a non-singular fast terminal sliding mode surface; Step 4.2: Design an equivalent control law and a switching control law to obtain the comprehensive control laws of the energy storage converter on the d-axis and q-axis.

[0021] Example 6 This example provides a backstepping sliding mode control method for a energy storage converter based on a cascaded generalized proportional-integral observer. On the basis of Examples 1-5, step 4.1 is specifically as follows: Let the deviation between the d-axis and q-axis current values after coordinate transformation and the reference values e 1, e 2 be: (13) In formula (13), i dref is i d 's reference value, i qref is i q 's reference value; To meet the system stability requirements, select the Lyapunov function V d , V q as: (14) And take the time derivative of formula (14) to get: (15) Define x d2 = p d , xq2 = p q , and based on the recursive design idea of the backstepping method, define the virtual control variables p d 、 p q as follows: (16) In formula (16), l 1, l 2 are the control parameters to be designed respectively; Define the error variables e 3, e 4 as follows: (17) And take the time derivative of formula (17) to get: (18) In formula (18), , ; Design the non-singular fast terminal sliding mode surface s d 、 s q as follows: (19) In formula (19), γ 1, γ 2, γ 3, γ 4 are the gains of the sliding mode surface and are positive real numbers; h 1, h 2, g 1, g 2 are all greater than 1 and less than 2, g 1> h 1, g 2> h 2; Step 4.2 is specifically Take the time derivative of formula (19) to get: (20) Based on the equivalent control method, design the equivalent control law u dreq 、 u qreq as follows: (21) Since formula (21) contains the virtual control quantity pd 、 p q In its derivative form, to avoid the phenomenon of differential explosion, the following second-order filter is introduced to estimate it: (22) In Equation (22), ε represents p d or p q ; τ 1, τ 2 are the filtering time constants; λ 1, λ 2, ρ 1, ρ 2 are the sliding mode filter constants to be designed; is p d or p q 's filtered value, is or 's estimated value; Furthermore, Equation (21) is re-expressed as: (23) In Equation (23), represents 's estimated value, represents 's estimated value; Taking the composite variable speed reaching law as the sliding mode switching control law, the d-axis and q-axis switching control laws are as follows: (24) In Equation (24), k 1, k 2, k 3 are the gains of the d-axis reaching law, k 4, k 5, k 6 are the gains of the q-axis reaching law, δ 1, δ 2 are variable exponential parameters, and the specific representation form is as follows: (25) In Equation (25), σ 1, σ 2 are both greater than 1, ε 1, ε 2 are both greater than 0 and less than 1, μ 1, μ 2 are both greater than 0, s d 、s q is the sliding mode surface; Combining the equivalent control law of Equation (23) and the switching control law of Equation (24), the comprehensive control law of the energy storage converter on the d-axis and q-axis is: (26).

[0022] Such as Figure 3 shown is the control schematic diagram of the backstepping sliding mode control method of the energy storage converter based on the cascaded generalized proportional integral observer of the present invention. The control method of the present invention has the following advantages: 1) The cascaded generalized proportional integral observer adopted by the control method of the present invention can improve the estimation accuracy of interference and can also effectively estimate various time-varying disturbances. The cascaded structure combines a linear observer and a nonlinear observer. The front-stage linear observer is used to ensure the stable operation of the system under large disturbances, and the rear-stage nonlinear observer is used to estimate the estimation residual of the front-stage disturbance, thereby further improving the anti-interference ability and noise suppression ability of the system.

[0023] 2) The design of the backstepping terminal sliding mode controller adopted by the control method of the present invention is to enhance the robust stability and asymptotic tracking ability of the system in the global process. Selecting a nonsingular terminal sliding mode control can effectively solve the singularity problem and make the system reach the vicinity of the sliding mode surface faster. In the sliding stage of the nonsingular terminal sliding mode, when the current error is far from the equilibrium point, the high-order term with the error integral term plays a major role; conversely, the high-order term of the error plays a major role. The combined effect of the two can make the current error converge rapidly to the equilibrium point along the sliding mode surface in a finite time. However, while the terminal sliding mode has good robustness, there is a problem that the transient performance of the system is not clear. Therefore, the backstepping method is used to ensure the stable performance of the system.

[0024] 3) The composite variable-speed reaching law adopted in the backstepping terminal sliding mode control of the present invention has the advantages of the exponential reaching law and the variable-power reaching law, and makes adaptive changes according to the change of the system sliding mode surface. When the motion trajectory of the controlled object is far from the equilibrium point, the δ value in the reaching law will be very large to ensure the speed of the sliding mode approaching motion. Conversely, when it is close to the equilibrium point, the approaching speed will continuously slow down. The second-order filter can be used to estimate the differential signal of the virtual control quantity in the backstepping method, avoid the differential explosion phenomenon existing in the backstepping method, and reduce the complexity of the backstepping terminal sliding mode controller.

[0025] Experimental analysis To verify the effectiveness of the backstepping sliding mode control method for the energy storage converter based on the cascaded generalized proportional integral observer in the energy storage converter model built on the Matlab / Simulink platform, to simulate the random switching of loads, when the active power undergoes a sudden change, it suddenly increases from the stable output of 20 kW to 70 kW at 0.25 s; it suddenly drops from the stable 70 kW to 20 kW at 0.3 s, and the dynamic response of the DC bus voltage fluctuation caused thereby. As Figure 4 shown, when the jump occurs at 0.25 s, the voltage jump amplitude of the PI control is 36 V, while the voltage jump of the control of the present invention is 12 V; when the jump occurs at 0.3 s, the voltage jump amplitude of the PI control is 33 V, while the voltage jump of the control of the present invention is 16 V. By comparing the transient DC bus voltage overshoot and regulation time under the two control strategies, it can be seen that although the PI control can control the bus voltage jump, its control ability is limited, while the control ability of the present invention can further improve the control ability of the bus voltage jump.

[0026] Define the power as positive when the voltage and current directions are the same, and the simulation parameters are set as shown in Table 1.

[0027] Table 1 Circuit parameters

[0028] To verify the influence of the control method of the present invention on the power quality of the output current of the energy storage converter, the grid-side b phase current of the three-phase inverter with an output active power of 20 kW was subjected to Fourier analysis for 2 steady-state cycles in the Matlab / Simulink software. As Figure 5 shown, it is the harmonic analysis of the grid-connected current of the energy storage converter under the traditional PI control, and the THD is 4.44%. Figure 6 shown is the harmonic analysis of the grid-connected current of the energy storage converter under the control of the present invention, and the THD is 0.57%. By comparison, it can be seen that the control method of the present invention has a stronger harmonic suppression ability and improves the power quality of grid connection.

[0029] To further verify the correctness of the simulation and theoretical content, an experiment was verified on a Hardware-In-the-Loop (HIL) experimental platform. The sampling frequency of the HIL was set to 20 kHz, the experimental platform was connected to the oscilloscope through an adapter board, and then the simulation circuit built in Simulink was loaded into the MT6020 and RCP1050 through the host computer to run for experimental verification.

[0030] Since the energy storage converter is in the grid-connected mode, the effective value of the phase voltage on the inverter side is fixed at 220 V. When the output active power of the energy storage converter jumps from 20 kW to 70 kW, bThe maximum value of the three-phase output current jumps from 43 A to 150 A. From Figure 7 it can be seen that under the PI control strategy, the voltage jump amplitude is 61 V, and the transition time reaches stability after 32 ms. From Figure 8 it can be seen that under the control method of the present invention, the voltage jump amplitude is 18 V, the transition time only needs 10 ms to reach stability, and the fluctuation of the DC bus voltage during steady-state operation is smaller than that of the PI control.

[0031] When the output active power of the energy storage converter jumps from 70 kW to 20 kW, b the maximum value of the three-phase output current jumps from 150 A to 43 A. From Figure 9 it can be seen that under the PI control strategy, the voltage jump amplitude is 58 V, and the transition time reaches stability after 29 ms. From Figure 10 it can be seen that under the control method of the present invention, the voltage jump amplitude is 8 V, the transition time only needs 8 ms to reach stability, and the fluctuation of the DC bus voltage during steady-state operation is smaller than that of the PI control.

[0032] In summary, the control method of the present invention based on the cascaded generalized proportional integral observer's backstepping terminal sliding mode effectively solves the problem that when the energy storage converter is affected by external time-varying disturbances in the grid-connected working mode, it can quickly restore the fluctuation of the DC bus voltage, improves the convergence speed and control accuracy of the energy storage converter, and effectively improves the power quality of the power grid.

Claims

1. A backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer, characterized in that, The implementation is specifically carried out according to the following steps: Step 1: Obtain the three-phase grid voltage and current using sensors, and use a phase-locked loop to control the magnitude and phase of the voltage to be consistent with the grid voltage. The reference grid-connected current in the rotating coordinate system is obtained by PQ control. Step 2: Subtract the actual grid-connected current from the reference grid-connected current to obtain the control error, and use a cascaded generalized proportional-integral observer to estimate the derivative of the system output value and the total disturbance; Step 3: Reconstruct the state-space model and design a cascaded generalized proportional-integral observer; Step 4: Design a backstepping terminal sliding mode controller; Step 5: Obtain the control output through the backstepping terminal sliding mode controller constructed in Step 4, use sinusoidal pulse width modulation (SPWM) to obtain the duty cycle, and apply the duty cycle to the control of the energy storage converter switching tubes, thereby realizing closed-loop control.

2. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 1, characterized in that The specific content of Step 1 is as follows: Under the condition of balanced three-phase grid voltage, according to Kirchhoff's law, the variable relationship of the energy storage converter in abc coordinate system is as follows: (1) In formula (1), u a , u b , u c are abc three-phase voltages, i La , i Lb , i Lc are the three-phase currents flowing through the inductor, abc three-phase currents, L , C are the inductor and capacitor filtering parameters respectively, R is the parasitic parameter of the filtering inductor, u ga , u gb , u gc are the abc voltages of the AC power grid, i a , i b , i c are the abc three-phase currents on the grid side; After coordinate transformation of Equation (1), the mathematical model of the AC side of the converter in the d-q coordinate system is: (2) In Equation (2), ω is the angular frequency of the grid voltage, u d , u q respectively represent the d-axis and q-axis components of the AC voltage, i Ld , i Lq respectively represent the d-axis and q-axis components of the inductor current, i d , i q respectively represent the d-axis and q-axis components of the grid-side current, u dr = s d u dc , u qr = s q u dc , s d , s q are the d-axis and q-axis switching functions respectively, and the switching functions are defined as: (3)。 3. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 2, characterized in that, The specific content of Step 2 is: On the basis of the three-phase balance of the grid voltage, take the d-axis direction of the grid voltage as the direction of the voltage vector. According to the instantaneous power theory, the power equation is obtained as: (4) In formula (4), P ref and Q ref are respectively the reference values of the set active power and reactive power, i dref and i qref are respectively the current reference values of the set active power and reactive power; The current reference values of active power and reactive power are respectively obtained from Equation (4) as: (5) Unify the internal and external disturbances and parameter perturbations of the system and represent them with lumped disturbances. Combining with Equation (2), we get: (6) In formula (6), b d and b q are the d-axis and q-axis control quantity gains respectively, f d and f q are the equivalent d-axis and q-axis lumped disturbances respectively. The lumped disturbance includes the unmodeled part of the system, the coupling part, and the internal and external disturbances of the system. The expressions for the d-axis and q-axis lumped disturbances are as follows: (7) Let the state variable x d1 = i Ld , x d2 = f d , x q1 = i Lq , x q2 = f q Then, Equation (6) is expressed in the following form: (8) To further improve the observation accuracy, expand the lumped disturbance, and the state-space model of Equation (8) is reconstructed as: （9）。 4. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 3, characterized in that, The specific content of Step 3 is: Definition z d11 、 z d12 、 z d13 、 z d14 、 z q11 、 z q12 、 z q13 、 z q14 are respectively x d1 、 x d2 、 f d 、 、 x q1 、 x q2 、 f q 、 observation values. According to Equation (9), the form of the first-stage generalized proportional-integral observer is designed as: (10) In Equation (10), β 11 , β 12 , β 13 , β 14 are the first-stage observer gains for the d-axis; h 11 , h 12 , h 13 , h 14 are the first-stage observer gains for the q-axis; To further estimate the disturbance error, take the first-stage estimated disturbance as the known part, and design the form of the second-stage generalized proportional-integral observer as: (11) In Equation (11), β 21 , β 22 , β 23 , β 24 are the gains of the d-axis of the second-stage observer; h 21 , h 22 , h 23 , h 24 are the gains of the q-axis of the second-stage observer; z d21 , z d22 , z d23 , z d24 are the observed values of the d-axis of the second-stage observer; z q21 , z q22 , z q23 , z q24 are the observed values of the q-axis of the second-stage observer, is a non-linear function.

5. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 4, characterized in that, The non-linear function has the following expression: (12) In formula (12), 0 < α i < 1, which is the exponential power coefficient; δ is a positive constant.

6. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 4, characterized in that The specific implementation of Step 4 is carried out according to the following steps: Step 4.1: Define the virtual control variable and the error variable, and design a non-singular fast terminal sliding mode surface; Step 4.2: Design the equivalent control law and the switching control law to obtain the comprehensive control law of the energy storage converter on the d-axis and q-axis.

7. The backstepping sliding mode control method for an energy storage converter based on a cascaded generalized proportional integral observer according to claim 6, characterized in that The specific content of Step 4.1 is: The deviation between the d-axis and q-axis current values after coordinate transformation and the reference values e 1、 e 2 is as follows: (13) In formula (13), i dref is i d 's reference value, i qref is i q 's reference value; To meet the system stability requirements, the Lyapunov function is selected V d , V q as follows: (14) Take the time derivative of Equation (14) to get: (15) Definition x d2 = p d , x q2 = p q and based on the recursive design idea of the backstepping method, define the virtual control variables p d 、 p q as follows: (16) In formula (16), l 1, l 2 are respectively control parameters to be designed; Define the error variable e 3, e 4 are as follows: (16) Take the time derivative of Equation (17) to get: (18) In formula (18), , ; Design a nonsingular fast terminal sliding mode surface according to Equation (18). s d 、 s q It is as follows: (19) In Equation (19), γ 1、 γ 2、 γ 3、 γ 4 is the gain of the sliding surface and is a positive real number; h 1、 h 2、 g 1、 g Both 1 and 2 are greater than 1 and less than 2, g 1> h 1, g 2> h 2.

8. The energy storage converter backstepping sliding mode control method based on a cascaded generalized proportional integral observer according to claim 7, characterized in that The specific content of Step 4.2 is: Take the time derivative of Equation (19) to get: (20) Based on the equivalent control method, design the equivalent control law according to Equation (20). u dreq 、 u qreq It is: (21) Since the virtual control quantity is included in Equation (21) p d and p q are in derivative form, to avoid the phenomenon of differential explosion, the following second-order filter is introduced to estimate them: (22) In formula (22), ε denotes p d or p q ; τ 1, τ 2 are the filter time constants; λ 1, λ 2, ρ 1, ρ 2 are the sliding mode filter constants to be designed; is p d or p q 's filtered value, is or 's estimated value; Furthermore, Equation (21) is re-expressed as: (23) In formula (23), represents the estimated value of, represents the estimated value of; Taking the composite variable speed reaching law as the sliding mode switching control law, the switching control laws on the d-axis and q-axis are as follows: (24) In formula (24), k 1,[[]]END]] k 2,[[]]END]] k 3 is the gain of the d-axis reaching law,[[]]END]] k 4,[[]]END]] k 5,[[]]END]] k 6 is the gain of the q-axis reaching law,[[]]END]] δ 1,[[]]END]] δ 2 is a variable exponential parameter, and its specific representation is as follows:[[]]END]] (25) In formula (25), σ 1, σ 2 are both greater than 1, ε 1, ε 2 are both greater than 0 and less than 1, μ 1, μ 2 are both greater than 0, s d , s q are sliding mode surfaces; Combining the equivalent control law of Equation (23) and the switching control law of Equation (24), the comprehensive control law of the energy storage converter on the d and q axes is u dr , u qr : (26)。

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