Active power filter and filtering method based on fractional order sliding mode control

Abstract

The application relates to the technical field of active power filtering, and particularly discloses an active power filter based on fractional order sliding mode control and a filtering method, the freedom of design is larger by designing a fractional order sliding mode surface and introducing the freedom of fractional order; the tracking chattering phenomenon generated in the ordinary sliding mode control process is effectively relieved by replacing a traditional sign function with a tanh function. The fractional order sliding mode control can not only make the system converge in a limited time, but also has fast response speed and high reliability in tracking of a direct current side voltage and a harmonic current. The active power filter adopting the fractional order sliding mode control method can not only well eliminate harmonics generated by a nonlinear load, but also enable the compensated current to quickly enter a new steady state when the nonlinear load disturbance is added, and the direct current side voltage can also quickly recover to a steady state. Simulation experiment results prove that the fractional order sliding mode control method has good fast response and robustness, and improves the dynamic and static performance of the system.

Description

Technical Field

[0001] This invention relates to the field of active power filtering technology, and in particular to an active power filter and filtering method based on fractional sliding mode control. Background Technology

[0002] With the widespread use of power electronic equipment in power systems and the integration of nonlinear loads, the power quality problems caused by harmonic pollution are becoming increasingly prominent. Furthermore, smelting enterprises, in order to achieve power factor standards and comply with power supply bureau requirements, often connect capacitors of a certain capacity in parallel to improve the power factor. However, at certain frequencies, this parallel resonance condition may be met, causing harmonic amplification and generating dangerous overvoltages or overcurrents. This often leads to substandard power quality at the point of common coupling, severely impacting the use of electrical appliances by surrounding users and the safe operation of the power system. In addition, when harmonic currents flow in the power grid, they cause active power loss and overheating in the lines. Severe harmonic problems can also reduce the breaking capacity of circuit breakers and cause malfunctions.

[0003] Currently, there are two main methods for suppressing harmonics: First, improving the power electronic devices themselves to reduce harmonic generation during power conversion and maximize the power factor. This method is suitable when power electronic equipment is the primary source of harmonics. Second, using filter devices, which are mainly divided into passive and active filters. For controlling low-order harmonics, single-tuned filters are used; for controlling high-order harmonics, high-pass filters are primarily used. However, passive filters have limited compensation characteristics. When harmonics in the power system change, passive power filters cannot dynamically adjust to the actual situation, significantly reducing their filtering effect and thus greatly limiting their application. Compared to passive filters, active filters offer advantages such as rapid tracking and dynamic compensation of harmonic currents and a wider dynamic range of harmonic filtering. Therefore, active power filters, as an effective device for suppressing harmonics and improving power grid quality, are widely used in harmonic control.

[0004] Currently, active power filters employ diverse models and a wide variety of control methods, resulting in the lack of an advanced control theory system for active power filters and consequently, lower system stability and reliability. To address this, the applicant filed an invention patent application on May 9, 2023, entitled "Active Power Filter and Filtering Method Based on First-Order PI-Sliding Membrane Control." This patent uses PI as the sliding surface and replaces the traditional sign function with the tanh function, effectively mitigating the tracking chattering phenomenon generated during ordinary sliding membrane control. Although this scheme has reduced the harmonic distortion rate of the compensated power supply current to 1.79%, there is still room for improvement. Summary of the Invention

[0005] This invention provides an active power filter and filtering method based on fractional sliding mode control. The technical problem it solves is that the harmonic distortion rate of the active power filter and filtering method based on first-order PI sliding mode control is still slightly high.

[0006] To solve the above technical problems, the present invention provides an active power filter based on fractional sliding mode control, including a DC power supply, a filter capacitor C, and an inverter connected in sequence. The three output terminals of the inverter are respectively connected to the three-phase power bus through an inductor L and a resistor r in series. The key feature is that the active power filter also includes a DC side voltage PID controller, a harmonic separation module, a current tracking controller, and a PWM drive module.

[0007] The DC-side voltage PID controller is used to control the output voltage U of the DC power supply based on the PID control principle. dc Stabilized at reference voltage U ref This addresses the impact of DC-side voltage fluctuations on the stable operation of active power filters (APFs).

[0008] The harmonic separation module is used based on the instantaneous power theory in i p -i q Algorithm to separate three-phase harmonic currents from grid voltage and current;

[0009] The current tracking controller is used to take the difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, as input, and calculate the corresponding control signal based on the fractional sliding mode control principle and output it to the PWM drive module.

[0010] The PWM drive module is used to drive the inverter based on the control signal.

[0011] Preferably, the current tracking controller includes a fractional-order sliding surface module, a robust switching module, and a fractional-order sliding controller:

[0012] The fractional sliding surface module is used to select the following fractional sliding surface s, i.e., s(t):

[0013]

[0014] Where β is the exponent, 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is e β The coefficients of (t), D is the differential operator, (0,x) is the fractional integral interval; e(t) is the three-phase harmonic current tracking error related to time t, expressed as: Right now For the three-phase harmonic currents related to time t, i k (t) i k The three-phase current output from the inverter and connected to the three-phase bus is the three-phase current. for The time-domain representation, i k (t) is i k The time-domain representation, k = a, b, c corresponds to phase a, phase b, and phase c, respectively;

[0015] The robust switching module is used to select a sliding mode convergence law such as:

[0016]

[0017] in, Let be the derivative of s, k1 and k2 are both constants greater than 0, and tanh() is the hyperbolic tangent function;

[0018] The fractional sliding mode controller is used to calculate the control function u based on the fractional sliding surface s and the sliding mode reaching law, using the Lyapunov function as the stability function;

[0019] The PWM drive module is used to select the system dynamics function based on the control function u and calculate the corresponding control signal to be applied to the three arms of the inverter.

[0020] Preferably, the control function u selected by the fractional-order sliding mode controller is:

[0021]

[0022] in, Indicates control gain. Represents three-phase harmonic current The derivative,

[0023] U represents the system function. sk k = a, b, c are the three-phase power supply voltages of a, b, c.

[0024] Preferably, the system dynamics function selected by the PWM drive module is:

[0025]

[0026] Where x = i k For state variables, Let ρ be the derivative of the state variable, h be the nonlinear load disturbance, and |h| < ρ, ρ > 0, where ρ is the upper bound of the disturbance.

[0027] This invention also provides an active power filtering method based on fractional sliding mode control, the key of which includes the following steps:

[0028] S1. An inverter is used, and the three output terminals of the inverter are connected to the three-phase power bus through an inductor L and a resistor r connected in series, respectively. The front end of the inverter is connected to the DC power supply through a filter capacitor C.

[0029] S2. Based on the PID control principle, control the output voltage U of the DC power supply. dc Stabilized at reference voltage U ref ;

[0030] S3, i based on instantaneous power theory p -i q Algorithm to separate three-phase harmonic currents from grid voltage and current;

[0031] S4. The difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, is used as input, and the corresponding control signal is calculated based on the fractional sliding mode control principle.

[0032] S4. Drive the inverter based on the control signal.

[0033] Furthermore, step S3 specifically includes the following steps:

[0034] S31. Design the following fractional sliding surface s, i.e., s(t):

[0035]

[0036] Where β is the exponent, 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is e β The coefficients of (t), D is the differential operator, (0,x) is the fractional integral interval; e(t) is the three-phase harmonic current tracking error related to time t, expressed as: Right now For the three-phase harmonic currents related to time t, i k (t) i k The three-phase current output from the inverter and connected to the three-phase bus is the three-phase current. for The time-domain representation, i k (t) is i k The time-domain representation, k = a, b, c corresponds to phase a, phase b, and phase c, respectively;

[0037] S32. Choose the following sliding mode convergence law:

[0038]

[0039] in, Let be the derivative of s, k1 and k2 are both constants greater than 0, and tanh() is the hyperbolic tangent function;

[0040] S33. Based on the fractional sliding surface s and the sliding mode reaching law, the Lyapunov function is used as the stability function, and the control function u is selected.

[0041] S34. Based on the control function u, the system dynamics function is selected and calculated to obtain the corresponding control signal applied to the three arms of the inverter.

[0042] Further, in step S33, the selected control function u is:

[0043]

[0044] Indicates control gain. Represents three-phase harmonic current The derivative, U represents the system function. sk k = a, b, c are the three-phase power supply voltages of a, b, c.

[0045] Further, in step S34, the selected system dynamics function is:

[0046]

[0047] Where x = i k For state variables, Let ρ be the derivative of the state variable, h be the nonlinear load disturbance, and |h| < ρ, ρ > 0, where ρ is the upper bound of the disturbance.

[0048] This invention provides an active power filter and filtering method based on fractional-order sliding mode control. By designing a fractional-order sliding surface and replacing the traditional sign function with a hyperbolic tangent function, the tracking chattering phenomenon generated during ordinary sliding mode control is effectively alleviated. Fractional-order sliding mode control not only allows the system to converge within a finite time but also exhibits fast response and high reliability in voltage and current tracking. The active power filter using fractional-order sliding mode control effectively eliminates harmonics generated by nonlinear loads, achieving a harmonic distortion rate as low as 0.79%, and also meets high stability requirements. Simulation results demonstrate that the fractional-order sliding mode control method has good fast response and robustness, improving the dynamic and static performance of the system. Attached Figure Description

[0049] Figure 1This is an overall schematic diagram of the active power filter provided in an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of a fractional sliding mode controller provided in an embodiment of the present invention;

[0051] Figure 3 This is a spectrum diagram of the current before filtering provided in an embodiment of the present invention;

[0052] Figure 4 This is a curve showing the actual output of the compensation current tracking the expected curve provided in an embodiment of the present invention.

[0053] Figure 5 This is a current diagram after compensation of the power grid current provided in an embodiment of the present invention;

[0054] Figure 6 This is a spectrum diagram of the filtered current provided in an embodiment of the present invention;

[0055] Figure 7 This is a dynamic diagram of DC-side voltage provided in an embodiment of the present invention. Detailed Implementation

[0056] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0057] The active power filter based on fractional-order sliding mode control provided in this embodiment of the invention has the following control principle: Figure 1 , Figure 2 As shown, the main function is to filter harmonics from the three-phase power supply using an inverter. Overall, this active power filter includes a DC power supply, a filter capacitor C, and an inverter connected in sequence. The three output terminals of the inverter are connected to the three-phase power bus via an inductor L and a resistor r connected in series. To control the inverter's conduction angle, the active power filter also includes a DC-side voltage PID controller, a harmonic separation module, a current tracking controller, and a PWM drive module.

[0058] Specifically, the DC-side voltage PID controller, based on the PID control principle, controls the output voltage U of the DC power supply. dc Stabilized at reference voltage U ref To address the impact of DC-side voltage fluctuations on the stable operation of the APF (Active Power Filter);

[0059] The harmonic separation module is based on the i in instantaneous power theory. p -i qAlgorithm to separate three-phase harmonic currents from grid voltage and current;

[0060] The current tracking controller takes the difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, as input, and calculates the corresponding control signal based on the fractional sliding mode control principle and outputs it to the PWM drive module.

[0061] The PWM drive module drives the inverter based on control signals.

[0062] The mathematical model of the active power filter is established based on circuit principles and Kirchhoff's theorem:

[0063]

[0064] Among them, U sa U sb U sc This refers to the three-phase power supply voltage (a, b, c), where O is the three-phase voltage reference ground point, and U... aN U bN U cN These are the line voltages between points a, b, and c on the AC side of the three-phase inverter and the voltage at point N; U NO It is the line voltage between point N and the reference ground point O, i k Let k = a, b, c be the three-phase currents (as compensation currents) output by the inverter connected to the three-phase bus. Assuming the grid voltage is balanced across the three phases, we can derive:

[0065] 3U NO +U aN +U bN +U cN =0 (2)

[0066] Summarized as follows:

[0067]

[0068]

[0069] U dc For DC side voltage, d k (k = a, b, c) is the switching function of the inverter IGBT (Insulated Gate Bipolar Transistor), representing the on / off state of the main circuit switching devices, specifically defined as:

[0070]

[0071] The dynamic model of the active power filter is as follows:

[0072]

[0073] Among them, Sk (k = a, b, c) is the control function:

[0074]

[0075] Get S k The expression for the nonlinear matrix:

[0076]

[0077] The dynamic model is transformed into the following form:

[0078]

[0079] Wherein, the state variable is x = i k , Represents system functions. Represents the control gain, u = S k Let h be the control function, h be the nonlinear load disturbance, and |h| < ρ, ρ > 0, where ρ is the upper bound of the disturbance. Let x be the derivative.

[0080] refer to Figure 2 The current tracking controller designed in this example includes a fractional sliding surface selection module, a robust switching module, and a fractional sliding controller.

[0081] The sliding surface selection module selects the following fractional-order sliding surface s, i.e., s(t):

[0082]

[0083] Where β is the exponent, 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is e β The coefficients of (t), D is the differential operator, and (0,x) is the interval of fractional-order calculus. e(t) is the three-phase harmonic current tracking error related to time t, expressed as: Right now For the three-phase harmonic currents related to time t, i k (t) i k k = a, b, c correspond to phase a, phase b, and phase c, respectively.

[0084] This example demonstrates the design of a fractional-order sliding surface, which introduces the fractional degree of freedom, thereby improving the design freedom and the response speed of the control system. As long as there is an error in the harmonic current tracking, the controller can quickly generate a control action.

[0085] Robust switching module selection is achieved using the sliding mode convergence law:

[0086]

[0087] in, Let be the derivative of s, k1 and k2 are both constants greater than 0, and tanh() is the hyperbolic tangent function.

[0088] The fractional sliding mode controller is based on the fractional sliding surface s and the sliding mode reaching law, and uses the Lyapunov function as the stability function to calculate the control function u.

[0089] In this example, the Lyapunov function is chosen as the stability function for the sliding mode control strategy design, that is:

[0090]

[0091] Where V(t) is the generalized energy function.

[0092] Differentiating V(t), i.e., V, we get:

[0093]

[0094] Prove system stability:

[0095]

[0096]

[0097] Take control function but:

[0098]

[0099] When k1 > 0 and k2 > 0, the system meets the stability condition.

[0100] Proof within a finite time frame:

[0101] When the system enters the sliding mode, setting s = 0, we get:

[0102]

[0103] Equation (17) can be transformed to obtain:

[0104]

[0105] Multiply both sides of equation (18) by e. -β (t) yields:

[0106]

[0107] Integrating both sides of equation (19) simultaneously, we get:

[0108]

[0109] Where, e(t) m ) represents the initial value of the harmonic current tracking error entering the sliding mode, t m t is the time when the harmonic current tracking error enters the sliding mode. n This is the moment when the harmonic current tracking error converges to a steady state. |e(t) m )|for t m The absolute value of the error at time t, |e(t) n )|for t n The absolute value of the error at time t. When the harmonic tracking error converges to a steady state, the absolute value of the tracking error tends to 0, i.e., |e(t) n )|=0.

[0110] According to the relevant definitions and lemmas of Riemann–Liouville type fractional calculus, we can obtain:

[0111]

[0112]

[0113] Where Γ(μ) (μ=α / 1+α / 1-β / α+1-β / 1) is the Gamma function, defined as:

[0114]

[0115] B(μ,v) (μ=α,ν=1) is the Beta function, and its expression is:

[0116]

[0117] Furthermore, the relationship between the Beta function and the Gamma function is as follows:

[0118]

[0119] According to equations (20) to (25), we can obtain the following through calculation:

[0120]

[0121] Through the above calculation process, it was finally concluded that finite-time control of the system was achieved.

[0122] Therefore, the control function u selected for the fractional-order sliding mode controller in this example is set as follows:

[0123]

[0124] The PWM drive module selects the system dynamics function based on the control function u and calculates the corresponding control signals to act as the three arms of the inverter.

[0125] The system dynamics function selected by the PWM drive module is:

[0126]

[0127] Where x = i k For state variables, Let ρ be the derivative of the state variable, h be the nonlinear load disturbance, and |h| < ρ, ρ > 0, where ρ is the upper bound of the disturbance.

[0128] exist Figure 2 It can also be seen that the DC-side voltage PID controller will be based on U dc and U ref The active current input harmonic separation module is obtained by PI calculation based on the difference ΔU. The harmonic separation module is based on U... sk (Uncompensated three-phase grid voltage) and i Lk Harmonic currents are separated from the three-phase grid current after compensation.

[0129] Corresponding to the above system, this embodiment of the invention also provides an active power filtering method based on fractional sliding mode control, including the following steps:

[0130] S1. Use an inverter and connect the three output terminals of the filter to the three-phase power bus through series inductor L and resistor r respectively, and connect the front end of the inverter to the DC power supply through filter capacitor C.

[0131] S2. Based on the PID control principle, control the output voltage U of the DC power supply. dc Stabilized at reference voltage U ref ;

[0132] S3, i based on instantaneous power theory p -i q An algorithm is used to separate three-phase harmonic currents from grid voltage and current.

[0133] S4. The difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, is used as input to calculate the corresponding control signal.

[0134] S4, Inverter driven by control signals.

[0135] Step S3 specifically includes the following steps:

[0136] S31. Choose the following fractional sliding surface s, i.e., s(t):

[0137]

[0138] Where 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is e β The coefficients of (t), D is the differential operator, and (0,x) is the interval of fractional-order calculus. e(t) is the three-phase harmonic current tracking error related to time t, expressed as: Right now For the three-phase harmonic currents related to time t, i k (t) i k k = a, b, c correspond to phase a, phase b, and phase c, respectively;

[0139] S32. Choose the following sliding mode convergence law:

[0140]

[0141] in, Let be the derivative of s, k1 and k2 are both constants greater than 0, and tanh() is the hyperbolic tangent function;

[0142] S33. Based on the fractional sliding surface s and the sliding mode reaching law, the Lyapunov function is used as the stability function, and the control function u is selected.

[0143] S34. Based on the control function u, the system dynamics function is selected for calculation, and the corresponding control signals are used as the three arms of the inverter.

[0144] In step S33, the selected control function u is:

[0145]

[0146] In step S34, the selected system dynamics function is:

[0147]

[0148] The active power filter and filtering method based on fractional-order sliding mode control provided in this invention design a fractional-order sliding surface and replace the traditional sign function with the tanh function, effectively mitigating the tracking chattering phenomenon generated during ordinary sliding mode control. Fractional-order sliding mode control not only allows the system to converge within a finite time but also exhibits fast response speed and high reliability in voltage and current tracking. The active power filter using the fractional-order sliding mode control method can effectively eliminate harmonics generated by nonlinear loads and also meets high stability requirements.

[0149] The simulation verification will be performed below.

[0150] This example is compared to Figure 1 , Figure 2An active power filter model was built using the SIMULINK simulation software in the MATLAB toolbox. A 220V / 50Hz equivalent system was used, with resistors R and inductors L simulating a nonlinear load. The principle of instantaneous reactive power was used to separate the fundamental and harmonic frequencies in the power grid. The current tracking module employed fractional-order sliding mode control, and the DC-side voltage used PID control. Figure 3 This is the current spectrum before filtering. It can be seen that the total distortion rate (THD) of the current is 21.75%, which is significantly higher than the national standard.

[0151] The time-domain response curve of the compensation current tracking the desired curve is shown in the figure below. Figure 4 As shown, the active power filter exhibits a good fast response at the start of operation (0.04s), and basically achieves current tracking after 0.03s. After adding a nonlinear load at 0.15s, the deviation tends to stabilize within one cycle. Overall, the compensation current tracks the commanded current well, and the deviation is within a reasonable range. Therefore, the effectiveness of the fractional-order sliding mode control method has been clearly verified.

[0152] Figure 5 This is the time-domain response curve after the grid current has been compensated. Using an active filter with fractional-order sliding mode control, the current waveform becomes smoother after 0.08s. At 0.15s, a nonlinear load is added as a disturbance, and it can be seen that the current amplitude changes, but the smoothness remains unchanged. The period from 0.04s to 0.07s is the transition process; effective current compensation begins at 0.07s. Figure 6 This is the filtered current spectrum. Figure 6 It can be seen that the harmonic distortion rate of the compensated power supply current is only 0.89% from 0.08s to 0.15s. When a nonlinear load is added at 0.15s, the harmonic distortion rate of the power supply current recovers to 0.89% after one cycle. Therefore, the active power filter using the fractional-mode sliding mode control method can not only effectively eliminate harmonics generated by nonlinear loads, but also meet high stability requirements. Simulation results demonstrate that the fractional-mode sliding mode control method has good fast response and robustness, improving the dynamic and static performance of the system.

[0153] Figure 7 The diagram shows the dynamic response of the DC-side voltage when a nonlinear load disturbance is applied at 0.15s. Figure 7 As can be seen, after the disturbance is added, approximately 0.04 seconds later, the DC side voltage U... dc The reference value Uref was reached again, and the overshoot was small, indicating that the system was stabilizing.

[0154] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. An active power filter based on fractional-order sliding mode control, comprising a DC power supply, a filter capacitor C, and an inverter connected in sequence, wherein the three output terminals of the inverter are respectively connected to a three-phase power bus through a series inductor L and a resistor r, characterized in that, The active power filter also includes a DC-side voltage PID controller, a harmonic separation module, a current tracking controller, and a PWM drive module; The DC-side voltage PID controller is used to control the output voltage U of the DC power supply based on the PID control principle. dc Stabilized at reference voltage U ref ; The harmonic separation module is used based on the instantaneous power theory in i p -i q Algorithm to separate three-phase harmonic currents from grid voltage and current; The current tracking controller is used to take the difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, as input, and calculate the corresponding control signal based on the fractional sliding mode control principle and output it to the PWM drive module. The current tracking controller includes a fractional sliding surface module, a robust switching module, and a fractional sliding controller: The fractional sliding surface module is used to select the following fractional sliding surface s, i.e., s(t): ， Where β is the exponent, 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is The coefficients, D is the differential operator, and (0,x) is the interval of fractional-order calculus; The three-phase harmonic current tracking error related to time t is expressed as follows: , Right now For the three-phase harmonic currents related to time t, Right now The three-phase current output from the inverter and connected to the three-phase bus is the three-phase current. for The time domain representation, for The time-domain representation, k=a,b,c corresponds to phase a, phase b, and phase c, respectively; The robust switching module is used to select a sliding mode convergence law such as: ， in, The derivative of s, and All are constants greater than 0. It is the hyperbolic tangent function; The fractional sliding mode controller is used to calculate the control function u based on the fractional sliding surface s and the sliding mode reaching law, using the Lyapunov function as the stability function; The PWM drive module is used to select the system dynamics function based on the control function u and calculate the corresponding control signal to be applied to the three arms of the inverter. The control function u selected by the fractional-order sliding mode controller is: ， in, Indicates control gain. Represents three-phase harmonic current The derivative, Represents system functions. The voltage of the three-phase power supply (a, b, c) is _____. The PWM drive module is used to drive the inverter based on the control signal.

2. The active power filter based on fractional-order sliding mode control according to claim 1, characterized in that, The system dynamics function selected by the PWM drive module is: ， in, For state variables, Let be the derivative of the state variable, and h be the nonlinear load disturbance. , This is the upper bound of the perturbation.

3. An active power filtering method based on fractional-order sliding mode control, applied to the active power filter based on fractional-order sliding mode control as described in claim 1 or 2, characterized in that, Including the following steps: S1. An inverter is used, and the three output terminals of the inverter are connected to the three-phase power bus through an inductor L and a resistor r connected in series, respectively. The front end of the inverter is connected to the DC power supply through a filter capacitor C. S2. Based on the PID control principle, control the output voltage U of the DC power supply. dc Stabilized at reference voltage U ref ; S3, i based on instantaneous power theory p -i q Algorithm to separate three-phase harmonic currents from grid voltage and current; S4. The difference between the three-phase harmonic current and the inverter output three-phase current, i.e. the harmonic current tracking error, is used as input, and the corresponding control signal is calculated based on the fractional sliding mode control principle. S5. Drive the inverter based on the control signal.

4. The active power filtering method based on fractional-order sliding mode control according to claim 3, characterized in that, Step S3 specifically includes the following steps: S31. Design the following fractional sliding surface s, i.e., s(t): ， Where β is the exponent, 0 < β < 1, α is the fractional order, 0 < α < 2, and C1 > 0 is the fractional derivative. The coefficient, C2>0 is The coefficients, D is the differential operator, and (0,x) is the interval of fractional-order calculus; The three-phase harmonic current tracking error related to time t is expressed as follows: , Right now For the three-phase harmonic currents related to time t, Right now The three-phase current output from the inverter and connected to the three-phase bus is the three-phase current. for The time domain representation, for The time-domain representation, k=a,b,c corresponds to phase a, phase b, and phase c, respectively; S32. Choose the following sliding mode convergence law: ， in, The derivative of s, and All are constants greater than 0. It is the hyperbolic tangent function; S33. Based on the fractional sliding surface s and the sliding mode reaching law, the Lyapunov function is used as the stability function, and the control function u is selected. S34. Based on the control function u, the system dynamics function is selected and calculated to obtain the corresponding control signal applied to the three arms of the inverter.

5. The active power filtering method based on fractional-order sliding mode control according to claim 4, characterized in that, In step S33, the selected control function u is: ， Indicates control gain. Represents three-phase harmonic current The derivative, Represents system functions. The voltages are for the three-phase power supply (a, b, c).

6. The active power filtering method based on fractional-order sliding mode control according to claim 5, characterized in that, In step S34, the selected system dynamics function is: ， in, For state variables, Let be the derivative of the state variable, and h be the nonlinear load disturbance. , This is the upper bound of the perturbation.

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