Control method of photovoltaic VSG inverter based on improved reaching law integral sliding mode

Abstract

The application relates to the field of photovoltaic power generation technology and discloses a control method of a photovoltaic VSG inverter based on an improved reaching law integral sliding mode, which aims to enhance the robustness and steady-state accuracy of a photovoltaic grid-connected VSG system.The control method of the photovoltaic VSG inverter based on the improved reaching law integral sliding mode is characterized in that a feedforward decoupling control is performed on a three-phase inverter mathematical model in a dq coordinate system, single control of dq-axis voltage and current is realized, a backstepping method is used to compensate for non-matching uncertain disturbance in the system, an integral sliding mode controller is designed for a voltage outer loop and a current inner loop subsystem, and the fast response of inverter d-axis current, active power and reactive power and the accurate tracking of the actual value and the reference value of the d-axis current under the condition of external disturbance and internal parameter perturbation are realized.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic power generation technology. Background Technology

[0002] With dwindling fossil reserves and increasing energy demand, new energy power generation has become an inevitable trend. In 2022, the newly installed capacity of wind and photovoltaic power generation in China exceeded 120 million kilowatts, setting a new historical record. Wind and photovoltaic power generation reached 11,900 kilowatt-hours, a year-on-year increase of 21%. New energy power generation can alleviate the pressure on traditional energy supply, reduce greenhouse gas emissions, and promote the development of a low-carbon economy. As a typical representative of new energy power generation, the development of the photovoltaic industry is of great significance to low-carbon and environmental protection. In recent years, economic incentives have driven the rapid expansion of the photovoltaic industry. In the first quarter of 2023, my country's cumulative inverter exports reached 3.118 billion yuan, a year-on-year increase of 137.4%, and a 3.6% increase compared to the fourth quarter of 2022, maintaining a high-speed growth trend.

[0003] Grid-connected photovoltaic (PV) VSG (Virtual Synchronous Generator) systems, as typical unmatched and uncertain systems, are microgrids composed of photovoltaic power sources and power electronic devices, similar to traditional synchronous generators. This system can operate in islanded and grid-connected modes, and controllable microgrid power generation can be achieved through appropriate control methods. However, in actual operation, nonlinear loads, uncertainties caused by PV module fluctuations, and parameter perturbations from multiple power electronic devices can severely affect system stability. Uncertainties arise from the outer-loop voltage system, source-end output, and DC regulation; these unmatched uncertainties cannot be compensated for by the system itself, leading to output voltage fluctuations and steady-state errors. Therefore, it is crucial to propose a control method that enhances robustness and steady-state accuracy for unmatched nonlinear systems like inverters in grid-connected PV VSG systems. Summary of the Invention

[0004] This invention aims to enhance the robustness and steady-state accuracy of photovoltaic grid-connected VSG systems. It provides a control method for photovoltaic VSG inverters based on an improved reaching law integral sliding mode.

[0005] The control method for photovoltaic VSG inverters based on improved reaching law integral sliding mode includes the following steps:

[0006] Step 1: Construct a mathematical model of the inverter based on an LC filter in a two-phase rotating coordinate system;

[0007] Step 2: Perform feedforward decoupling control on the voltage and current in the mathematical model based on the LC filter in the two-phase rotating coordinate system;

[0008] Step 3: Construct the voltage outer loop state equation and the current inner loop state equation considering parameter perturbations respectively;

[0009] Step 4: Design the integral sliding surface of the voltage outer loop based on the voltage outer loop state equation and the current inner loop state equation respectively. Integral sliding surface of the inner current loop

[0010] Step 5: Design novel composite reaching laws for the outer voltage loop. Novel Composite Approach Law of Current Inner Loop

[0011] Step Six: Perform voltage outer ring sliding mode tests on each surface. and the sliding surface of the inner current loop Find the first derivative, and then combine it with the novel composite reaching law of the voltage outer loop. Novel Composite Approach Law of Current Inner Loop By connecting these connections, a virtual control law for the outer voltage loop can be constructed. and the virtual control law u of the inner current loop i Using the virtual control law of the outer voltage loop and the virtual control law u of the inner current loop i By obtaining the outer voltage control signal and the inner current control signal, the photovoltaic virtual synchronous machine inverter can be controlled.

[0012] The voltage outer loop virtual control law The expression is as follows:

[0013]

[0014]

[0015]

[0016] The virtual control law of the current inner loop u i The expression is as follows:

[0017] u i =u ieq +u in ,

[0018]

[0019]

[0020] In the above formula, and These are the equivalent control law and the actual control law for the voltage outer loop, respectively. ieq and u in These are the equivalent control law and the actual control law for the inner current loop, respectively, with the intermediate variable f1 = -i0 / C. f The intermediate variable f2 = -R f ig -u g Intermediate variable g1 = -1 / C f , For u ref The first derivative, u ref The setpoint for the inverter output voltage. For voltage outer loop tracking error, For the current inner loop tracking error, i g and u g These represent the actual values ​​of the grid-side current and voltage, respectively; i0 represents the actual value of the inverter output current; C f and R f Let C'1 be the capacitor and C'2 be the resistor of the LC filter, respectively, p be the Laplace operator, and C'1, C'2, C1, and C2 be positive real numbers. η, k, a, and q are all constants, and sat() is a saturation function, expressed as: Δ represents the boundary layer and intermediate variables. γ is a saturation function variable.

[0021] Furthermore, in step one above, a mathematical model of the inverter in a three-phase stationary coordinate system is first established based on Kirchhoff's voltage and current laws:

[0022]

[0023] Among them, u abc and i abc These represent the three-phase output voltage and three-phase output current of the inverter, respectively. gabc and i gabc These are the three-phase output voltage and three-phase output current on the grid side, respectively. f The inductance of the LC filter in a three-phase stationary coordinate system;

[0024] Then, the mathematical model of the inverter in the three-phase stationary coordinate system is transformed to obtain the mathematical model of the inverter based on the LC filter in the two-phase rotating coordinate system.

[0025] Furthermore, the mathematical model expression for the above inverter based on the LC filter in a two-phase rotating coordinate system is as follows:

[0026]

[0027] Among them, u gd and u gq These are the actual d-axis and q-axis voltage values ​​on the grid side, i gd and i gq These are the actual d-axis and q-axis current values ​​on the grid side, u d and u q These are the actual d-axis and q-axis voltage values ​​of the inverter, id and i q ω represents the actual values ​​of the d-axis and q-axis currents of the inverter, respectively, and ω is the synchronous rotational angular velocity of the inverter.

[0028] Furthermore, the corner frequency of the aforementioned LC filter Satisfy the following formula:

[0029]

[0030] Where F is the fundamental frequency of the output waveform of the LC filter, f s This is the PWM modulation switching frequency.

[0031] Furthermore, in step two above, the voltage and current in the mathematical model based on the LC filter in the two-phase rotating coordinate system are subjected to feedforward decoupling control, so that the mathematical model of the inverter is transformed into:

[0032]

[0033] in, for The first derivative, u gref The setpoint for the grid-side voltage. For i g First derivative, intermediate variable L f Let u be the inductance of the LC filter in a three-phase stationary coordinate system, and let u be the actual value of the inverter output voltage.

[0034] Furthermore, in step three above, the voltage outer loop state equation and the current inner loop state equation considering parameter perturbations are constructed respectively, including:

[0035] Define the current inner loop tracking error The expression is:

[0036]

[0037] Based on the current inner loop tracking error Construct the voltage outer loop state equation:

[0038]

[0039] Based on the current inner loop tracking error Construct the state equation for the inner current loop:

[0040]

[0041] Among them, i gref Given the grid-side current, d u Let ΔL be the lumped uncertainty parameter of the voltage outer loop.f and ΔR f These are the inductor perturbation and resistor perturbation of the LC filter, respectively, R f0 and L f0 These are the initial values ​​of the resistor and inductor of the LC filter, respectively.

[0042] Furthermore, the above parameter perturbation is described as follows:

[0043]

[0044] Where, ΔR f ΔL f and ΔC f These are the perturbations of the LC filter's resistor, inductor, and capacitor, respectively, C. f0 This represents the initial value of the LC filter capacitor.

[0045] Furthermore, the lumped uncertainty parameter d of the aforementioned voltage outer loop... u The expression is:

[0046]

[0047] Furthermore, in step four above, the integral sliding surface of the voltage outer loop... Integral sliding surface of the inner current loop The expressions are as follows:

[0048]

[0049]

[0050] Furthermore, in step five above, the novel composite reaching law of the voltage outer loop... Novel Composite Approach Law of Current Inner Loop The expressions are as follows:

[0051]

[0052]

[0053] This invention proposes a control method for photovoltaic VSG inverters based on improved reaching law integral sliding mode. By performing feedforward decoupling control on the mathematical model of the three-phase inverter in the dq coordinate system, separate control of the dq axis voltage and current is achieved. The backstepping method is used to compensate for the unmatched uncertainty disturbance in the system. Integral sliding mode controllers are designed for the voltage outer loop and current inner loop subsystems to achieve fast response of inverter d-axis current, active power and reactive power under parameter perturbation and unmatched uncertainty disturbance, and accurate tracking of the actual value and reference value of d-axis current. Attached Figure Description

[0054] Figure 1 This is a flowchart of the control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode as described in this invention;

[0055] Figure 2 This is a structural model diagram of the inverter;

[0056] Figure 3 Block diagram of feedforward decoupling control principle for inverter

[0057] Figure 4 This is a block diagram illustrating the principle of the control method for a photovoltaic VSG inverter based on an improved reaching law integral sliding mode. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0059] Photovoltaic VSG inverter systems are subject to external disturbances such as parameter perturbations and changes in ambient temperature and humidity during operation. These disturbances can lead to slow d-axis current response, large current tracking errors, and significant power tracking errors in the inverter output. Traditional PI algorithms cannot compensate for the unmatched uncertainties in the system, resulting in large current amplitudes and severe waveform distortion. Sliding mode control, on the other hand, possesses strong robustness and anti-interference capabilities, capable of handling system parameter changes and external disturbances. Therefore, it is widely used in permanent magnet synchronous motors, robotics, and aerospace. However, while traditional sliding mode control algorithms can compensate for some of the unmatched uncertainties, they also exhibit significant chattering, placing higher demands on the controller.

[0060] To address the aforementioned issues, this implementation proposes an inverter control method for a photovoltaic virtual synchronous machine based on a reaching law integral sliding mode. Compared to traditional sliding mode, it replaces the original high-frequency switching term with an integral form control law, eliminating system chattering while retaining the robustness of sliding mode. (Refer to...) Figures 1 to 4 This embodiment specifically describes the inverter control method for a photovoltaic virtual synchronous machine based on a reaching law integral sliding mode, which includes:

[0061] Step S1) Build a mathematical model of the inverter in the photovoltaic VSG (virtual synchronous machine) system based on the LC filter in a two-phase rotating coordinate system, and simplify and determine the parameters of the mathematical model while ensuring the filtering performance of the model.

[0062] Specifically, a mathematical model of the inverter in a three-phase stationary coordinate system is established based on Kirchhoff's voltage and current laws:

[0063]

[0064] In the formula, L f R f C f These are the inductance, resistance, and capacitance of the LC filter, u abc and i abc These represent the three-phase output voltage and three-phase output current of the inverter, respectively. gabc and i gabc These are the three-phase output voltage and three-phase output current on the grid side, respectively.

[0065] Through coordinate transformation, the mathematical model expression of the inverter based on the LC filter in a two-phase rotating coordinate system can be obtained as follows:

[0066]

[0067] In the formula, L f R f C f These are the inductance, resistance, and capacitance of the LC filter, u gd and u gq These are the actual d-axis and q-axis voltage values ​​on the grid side, i gd and i gq These are the actual d-axis and q-axis current values ​​on the grid side, u d and u q These are the actual d-axis and q-axis voltage values ​​of the inverter, i d and i q ω represents the actual values ​​of the d-axis and q-axis currents of the inverter, respectively, and ω is the synchronous rotational angular velocity of the inverter.

[0068] While ensuring the basic functions of the LC filter, the control system parameters are simplified. The basic functions of the LC filter are to limit voltage fluctuations, eliminate harmonics, and enhance the sinusoidal intensity of the PWM modulation wave. The LC filter is a typical second-order system. Analyzing its amplitude-frequency characteristics, phase-frequency characteristics, and transfer function, it can be seen that the frequency is higher than the natural frequency ω. n The high-frequency harmonic attenuation is 40 dB / sec. The designed LC filter's corner frequency... It must be much greater than the fundamental frequency F (50Hz) of the output waveform, and much smaller than the PWM modulation switching frequency f. s In this implementation, the kHz frequency is set to 10kHz, which satisfies the following formula:

[0069]

[0070] Taking all factors into consideration, in order to filter out high-frequency signals from the PWM output, ensure stable low-frequency signal output, and optimize filtering effect and filter stability, the LC filter was ultimately determined to have an inductance of 3.5mH, a capacitance of 8μF, and a cutoff frequency of 952Hz.

[0071] Step S2) The inverter mathematical model in the two-phase rotating coordinate system (dq coordinate system) is coupled. To achieve independent control of the dq axis currents, feedforward decoupling control is required to eliminate inter-axis coupling. After dq feedforward decoupling, the inverter mathematical model in the dq coordinate system is transformed as follows:

[0072]

[0073] In the formula, the intermediate variable f1 = -i0 / C f f2 = -R f i g -u g i g and u g These are the actual values ​​of the grid-side current and voltage, respectively, and i0 is the actual value of the inverter output current.

[0074] g1 and g2 are the nonlinear gain matrices of the state variable and control variable, respectively, and are continuously differentiable, with the following condition: g1 = -1 / C f g2 = 1 / L f .

[0075] for The first derivative, This is the voltage outer loop tracking error, and there is... u ref This is the setpoint for the inverter output voltage.

[0076] and i g and u ref The first derivative.

[0077] u represents the actual value of the inverter's output voltage.

[0078] The active power P and reactive power Q of the inverter output after feedforward decoupling in the dq coordinate system are as follows:

[0079]

[0080] u gd and u gq These are the actual d-axis and q-axis voltage values ​​on the grid side, i d and i q These are the actual values ​​of the d-axis and q-axis currents of the inverter, respectively.

[0081] To meet the requirements of static stability and dynamic fast response of the inverter, same voltage vector control can be used, setting the grid-side q-axis voltage to 0. The above formula can be transformed into:

[0082]

[0083] Considering that the inverter is a typical second-order system, a dual closed-loop control with an outer voltage loop and an inner current loop is designed. The controller model after adding closed-loop control is as follows:

[0084]

[0085] Where, k p k is the proportionality coefficient. i Let be the integral coefficients, and s be the differential operator. and These are the reference values ​​for the d-axis and q-axis output currents of the inverter, respectively, and L is the line inductance of the inverter.

[0086] After passing through the outer voltage loop controller, the voltage tracking error converges to 0, and the inner loop current setpoint is output. After current decoupling and the inner current loop controller, the inverter's dq-axis output voltage u is output. d and u q The coordinate transformation yields the α and β axes, which are then used as output signals and modulated by SVPWM to output pulse signals.

[0087] Current inner loop transfer function G i (λ) is equivalent to:

[0088]

[0089] In the formula, T a H is the sampling time constant of the IGBT switch. i (λ) is the current inner loop feedback function, λ is the complex function variable, and δ is the complex frequency.

[0090] Compared to the inner current loop, the outer voltage loop changes more slowly, and the transfer function G of the outer voltage loop is... u (λ) is:

[0091]

[0092]

[0093] In the formula, e d T represents the error between the inverter output voltage and the voltage setpoint. c =T b +3T a T b U is the voltage sampling time constant. dc τ is the DC-side voltage of the inverter. bIt is a constant that satisfies τ b =K bp / K bI C is the inverter capacitor.

[0094] Step S3) When the inverter is running, factors such as component aging and changes in temperature and humidity can cause fluctuations in the parameters of resistance, capacitance, and inductance. These component parameter perturbations can be described as follows:

[0095]

[0096] In the formula, ΔR f ΔL f and ΔC f These are the perturbations of the LC filter's resistor, inductor, and capacitor, respectively, and each has an upper bound M. R M L and M C R f0 L f0 and C f0 These are the initial values ​​for the resistor, inductor, and capacitor of the LC filter, respectively.

[0097] In a grid-connected photovoltaic (PV) VSG system, the inverter is a typical unmatched nonlinear second-order system. Traditional PI algorithms cannot control parameters when perturbations occur in non-control signal channels, leading to reduced controllability and control accuracy. However, sliding mode control exhibits strong robustness and can effectively handle internal parameter perturbations and external disturbances, making it widely used in motor control, mechanical control, and autonomous driving. Furthermore, sliding mode control based on backstepping can address parameter perturbations in non-control signal channels, eliminating their impact on the controller.

[0098] To address the mismatch uncertainty caused by outer loop parameter perturbations, the current inner loop tracking error is defined.

[0099]

[0100] Among them, i gref This is the setpoint for the grid-side current.

[0101] Based on the aforementioned current inner loop tracking given error The state equations for constructing the outer voltage loop are as follows:

[0102]

[0103] In the formula, This is a virtual control law for the outer voltage loop, and it has...

[0104] d u The lumped uncertainty parameter of the voltage outer loop is expressed as:

[0105] In the state equation of the voltage outer loop, the PWM switching signal serves as the actual control input, and the control input and input gain are equivalent to the current inner loop control law u. i At this point, the state equation of the inner current loop is:

[0106]

[0107] Step S4) Design the integral sliding surface of the voltage outer loop based on the state equation of the voltage outer loop. for:

[0108]

[0109] In the formula, C1 and C2 are both positive real numbers, and it is necessary to ensure that the polynomial p 2 The real part of the eigenvalue of +C1p+C2=0 is negative, where p is the Laplace operator. In this embodiment, C1=C2=600.

[0110] To ensure the current inner loop tracks the given error e ig Both its derivatives converge to 0 in finite time. Design the inner loop integral sliding surface of the current. for:

[0111]

[0112] And it exists:

[0113] Step S5) Design a novel composite reaching law for the voltage outer loop.

[0114]

[0115] Design a novel composite approach law for the inner current loop.

[0116]

[0117] Step S6) Integral sliding surface of the outer voltage loop After finding the first derivative, a novel composite reaching law with the outer voltage loop is obtained. By connecting the loops, the outer loop control law of the voltage can be obtained. for:

[0118]

[0119] This is the equivalent control law for the outer voltage loop. The actual control law for the outer voltage loop is expressed as follows:

[0120]

[0121]

[0122] Integral sliding surface of the inner current loop After finding the first derivative, a novel composite reaching law with the inner current loop is obtained. By connecting the loops, the inner current control law u can be obtained. i for:

[0123] u i =u ieq +u in ,

[0124] In the formula, u ieq For the equivalent control law of the inner current loop, u in The actual control law for the inner current loop is expressed as follows:

[0125]

[0126]

[0127] In the above formula, the intermediate variable f1 = -i0 / C f The intermediate variable f2 = -R f i g -u g Intermediate variable g1 = -1 / C f , For u ref The first derivative, u ref The setpoint for the inverter output voltage. For voltage outer loop tracking error, For the current inner loop tracking error, i g and u g These represent the actual values ​​of the grid-side current and voltage, respectively; i0 represents the actual value of the inverter output current; C f and R f Let C'1 be the capacitor and C'2 be the resistor of the LC filter, respectively, p be the Laplace operator, and C'1 = C'2 = 600, where C1 and C2 are both positive real numbers. η > 0, 0 < a < 1, q > 0, and k are all constants. Within this range, they are adjusted according to the magnitude of the system disturbance to ensure that the output voltage and output current of the inverter system stably track the given values ​​with minimal overshoot. In this embodiment, k = 150, η = 20, q = 100, and a = 3 / 5.

[0128] sat() is a saturation function, expressed as: Δ represents the boundary layer. Switching control is used outside the boundary layer, while linearization control is used inside the boundary layer. Intermediate variables... γ is a saturation function variable.

[0129] Using the Lyapunov stability criterion It can be proven that the voltage outer loop tracking error It will reach the sliding surface within a limited time. And it converges to 0.

[0130] Finally, the voltage outer loop control law is used. and the inner loop control law u i The voltage outer loop and current inner loop of the inverter are controlled by the control signals respectively.

[0131] The Lyapunov stability criterion shows that the inner loop current will reach the designed integral sliding surface within a finite time, and the tracking virtual control law and the voltage outer loop tracking error will converge to 0. The designed integral terminal sliding controller based on backstepping can offset the unmatched uncertainty and improve the accuracy and robustness of voltage tracking and current tracking.

[0132] In summary, this embodiment discloses a control method for a photovoltaic VSG inverter based on an improved reaching law integral sliding mode. Compared with traditional PI and traditional sliding mode, it improves the tracking speed of output power during power surges, while reducing the ripple of output current and output power, thereby improving the control accuracy and robustness of the system.

[0133] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A control method for a photovoltaic VSG inverter based on an improved reaching law integral sliding mode, characterized in that, Includes the following steps: Step 1: Construct a mathematical model of the inverter based on an LC filter in a two-phase rotating coordinate system; Step 2: Perform feedforward decoupling control on the voltage and current in the mathematical model based on the LC filter in the two-phase rotating coordinate system; Step 3: Construct the voltage outer loop state equation and the current inner loop state equation considering parameter perturbations respectively; Step 4: Design the integral sliding surface of the voltage outer loop based on the voltage outer loop state equation and the current inner loop state equation respectively. Integral sliding surface of the inner current loop ; Step 5: Design novel composite reaching laws for the outer voltage loop. Novel Composite Approach Law of Current Inner Loop ; Step Six: Perform voltage outer ring sliding mode tests on each surface. and the sliding surface of the inner current loop Find the first derivative, and then combine it with the novel composite reaching law of the voltage outer loop. Novel Composite Approach Law of Current Inner Loop By connecting these connections, a virtual control law for the outer voltage loop can be constructed. and the virtual control law of the inner loop of the current Using the virtual control law of the outer voltage loop and the virtual control law of the inner loop of the current Obtain the outer voltage control signal and the inner current control signal to control the photovoltaic virtual synchronous machine inverter; The voltage outer loop virtual control law The expression is as follows: ， ， ， The virtual control law of the current inner loop The expression is as follows: ， ， ， In the above formula, and These are the equivalent control law and the actual control law for the voltage outer loop, respectively. and These are the equivalent control law and the actual control law for the inner current loop, respectively, with intermediate variables... intermediate variables intermediate variables , for The first derivative, The setpoint for the inverter output voltage. For voltage outer loop tracking error, For the current inner loop tracking error, and These are the actual values ​​of the grid-side current and voltage, respectively. This represents the actual value of the inverter output current. and These are the capacitor and resistor of the LC filter, respectively. For the Laplace operator, , , and All are positive real numbers. , , , and All are constants. Let be a saturation function, with the expression: , For boundary layer, intermediate variables , For saturated function variables; In step three, the voltage outer loop state equation and the current inner loop state equation considering parameter perturbations are constructed respectively, including: Define the current inner loop tracking error The expression is: ； Based on the current inner loop tracking error Construct the voltage outer loop state equation: ， Based on the current inner loop tracking error Construct the state equation for the inner current loop: ， in, The given value for the grid-side current. For the lumped uncertainty parameters of the voltage outer loop, and These are the inductor perturbation and the resistor perturbation of the LC filter, respectively. and These are the initial values ​​of the LC filter resistor and inductor, respectively. In step four, the integral sliding surface of the voltage outer loop Integral sliding surface of the inner current loop The expressions are as follows: ， ； In step five, the novel composite approach law of the voltage outer loop is described. Novel Composite Approach Law of Current Inner Loop The expressions are as follows: ， 。 2. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 1, characterized in that, In step one, a mathematical model of the inverter in a three-phase stationary coordinate system is first established based on Kirchhoff's voltage and current laws: ， in, and These are the three-phase output voltage and three-phase output current of the inverter, respectively. and These are the three-phase output voltage and three-phase output current on the grid side, respectively. The inductance of the LC filter in a three-phase stationary coordinate system; Then, the mathematical model of the inverter in the three-phase stationary coordinate system is transformed to obtain the mathematical model of the inverter based on the LC filter in the two-phase rotating coordinate system.

3. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 1 or 2, characterized in that, The mathematical model expression of the inverter based on the LC filter in a two-phase rotating coordinate system is as follows: ， in, and These are the actual d-axis and q-axis voltage values ​​on the grid side, respectively. and These represent the actual d-axis and q-axis current values ​​on the grid side, respectively. and These are the actual d-axis and q-axis voltage values ​​of the inverter, respectively. and These are the actual d-axis and q-axis current values ​​of the inverter, respectively. This refers to the synchronous rotational angular velocity of the inverter.

4. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 3, characterized in that, Corner frequency of LC filter Satisfy the following formula: ， in, The fundamental frequency of the output waveform of the LC filter. This is the PWM modulation switching frequency.

5. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 1, characterized in that, In step two, the voltage and current in the mathematical model based on the LC filter in the two-phase rotating coordinate system are subjected to feedforward decoupling control, so that the mathematical model of the inverter is transformed into: ， in, for The first derivative, The given value for the grid-side voltage. for First derivative, intermediate variable , The inductance of the LC filter in a three-phase stationary coordinate system is given. This is the actual value of the inverter output voltage.

6. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 1, characterized in that, The parameter perturbation is described as follows: ， in, , and These are the perturbations of the LC filter's resistor, inductor, and capacitor, respectively. This represents the initial value of the LC filter capacitor.

7. The control method for a photovoltaic VSG inverter based on improved reaching law integral sliding mode according to claim 6, characterized in that, The lumped uncertainty parameters of the voltage outer loop The expression is: 。

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