An adaptive ac fractional order filter

Abstract

This invention discloses an adaptive AC fractional-order filter, relating to the field of power quality technology, comprising: a controllable fractional-order capacitor and a harmonic inductor L connected in series. r The fractional-order filter is connected between the AC bus and ground, and to the load R. o They are connected in parallel; the controllable fractional-order capacitors include the output capacitor C. r Output inductor L f Switch S a S b S c S d and an energy storage capacitor C d Composition; Switching transistor S a With the switching transistor S b Series connection, switching transistor S c With the switching transistor S d They are connected in series and in parallel to the energy storage capacitor C. d Both ends; switching transistor S c With the switching transistor S d The connection point is connected via the output inductor L f Connected to output capacitor C r One end, the switching transistor S a With the switching transistor S b The connection point is directly connected to capacitor C. r On the other end, this invention achieves zero impedance to specific frequency subharmonics by constructing a filter containing controllable fractional-order capacitors, thereby suppressing low-frequency harmonic currents.

Description

Technical Field

[0001] This invention relates to the field of power quality technology, specifically to an adaptive AC fractional-order filter. Background Technology

[0002] In recent years, smart microgrids have developed rapidly, and various new power electronic converters and loads have been applied to microgrids. Some of these nonlinear loads introduce low-order harmonics into the power grid, especially the fifth and seventh current harmonics. Low-frequency harmonic distortion is one of the most significant power quality problems in modern smart grids. It increases core losses and temperature rise in equipment such as transformers and motors, shortens their service life, and causes overvoltage, overcurrent, and instability in the system, affecting system safety and stability. It also interferes with the normal operation of protection devices and measuring instruments, leading to malfunctions or failures to operate, resulting in low power factor, reduced efficiency, and increased line losses.

[0003] To better compensate for harmonics of varying magnitude and frequency, as well as varying reactive power, and to make power distribution systems more compatible with harmonic environments, active power filters, as a new type of power electronic device for dynamically suppressing harmonics and compensating for reactive power, are being widely used. Hybrid active power filters, which are derived from this technology, are currently a hot research topic. For example, the harmonic suppression effect of the filter can be enhanced by adding a notch filter and adjusting the filter parameters, thereby achieving effective suppression of higher-order harmonics. Alternatively, a passive decoupling capacitor can be split into an active capacitor connected in series with another passive decoupling capacitor, which not only provides a stable supply voltage to the load but also absorbs pulsating power and suppresses harmonic currents.

[0004] To address the aforementioned power quality issues, research on low-frequency harmonic suppression technology has been ongoing. Traditionally, passive filters have been used to compensate for reactive power and eliminate harmonic currents. For example, a pulse-width modulation inverter with an LC filter driving an induction motor can reduce its output high-frequency noise and harmonics; combining notch filters and LCL filters can achieve current harmonic filtering and reduce AC capacitor voltage fluctuations, and step-down circuits can be designed to address transformer saturation in weak power grids. However, the compensation capability and center frequency of passive filters are usually not adjustable, making them unsuitable for flexible and varied application scenarios. Furthermore, the parameters of passive devices change over time due to aging, and are affected by the scale of distributed micro-sources and the type of load, resulting in non-integer harmonics such as interharmonics in microgrids. Parameter deviations exist in various applications of power electronics, such as interleaved boost converters, electromagnetic interference filters, modular multilevel converters, and wireless power transfer. Meanwhile, variable capacitors, variable inductors, and high power factor circuits can adaptively adjust the inductor or capacitor values ​​to meet specific requirements based on different load conditions and harmonic interference frequencies through multiple variable units. However, these methods of compensating for parameter errors have the following problems: 1) Variable capacitors or inductors can only adjust reactance, without considering other parasitic parameters such as resistance; 2) In order to obtain a larger adjustable range, the voltage stress of the switching devices will increase significantly; 3) Error compensation of equipment parameters requires high control accuracy and calculation ability; 4) Such circuits are in the main filtering circuit, which means larger capacity and circuit loss. Summary of the Invention

[0005] In view of the above problems, the present invention provides an adaptive AC fractional-order filter. By constructing a filter containing a controllable fractional-order capacitor, zero impedance to specific frequency subharmonics is obtained, thereby suppressing low-frequency harmonic currents. The resonant frequency and minimum impedance of the filter are adjustable, thereby suppressing current harmonics with random fluctuations in frequency and amplitude. This fractional-order filter is not sensitive to device parameters and can maintain good harmonic suppression capability within a certain error range.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] An adaptive AC fractional-order filter includes: a controllable fractional-order capacitor and a harmonic inductor L connected in series. r The fractional-order filter is connected between the AC bus and ground, and to the load R. o They are connected in parallel;

[0008] The controllable fractional-order capacitor includes an output capacitor C. r Output inductor L f First switching transistor S a Second switch S b Third switch S cFourth open valve S d and an energy storage capacitor C d Composition; the first switching transistor S a With the second switching transistor S b The third switch S is connected in series. c With the fourth switch S d They are connected in series and in parallel to the energy storage capacitor C. d Both ends; the third switch S c With the fourth switch S d The connection point is connected via the output inductor L f Connected to output capacitor C r At one end, the first switch S a With the second switching transistor S b The connection point is directly connected to capacitor C. r The other end;

[0009] The voltage of the controllable fractional capacitor is controlled by a closed-loop voltage control, as follows;

[0010] For bus current i bus Harmonic detection is performed to separate the fundamental current and harmonic currents, and the harmonic amplitude I at this time is obtained. har Harmonic frequency f har With harmonic phase θ har ;

[0011] Based on harmonic amplitude I har Harmonic frequency f har The amplitude U of the suppressed harmonic modulation voltage is obtained. har ;

[0012] The normalized harmonic current is fed into an integration delay stage to obtain the frequency and phase of the suppressed harmonic modulation voltage, and the amplitude U of the harmonic modulation voltage. har Combining these methods yields a harmonic-suppressed modulation voltage;

[0013] The harmonic modulation voltage and AC power supply voltage u will be suppressed. s By superimposing the results, the output capacitance C is obtained. r Reference voltage u cr-ref ;

[0014] Reference voltage u cr-ref The difference between the output capacitor voltage (ucr) and the output capacitor voltage (ucr) is used to perform voltage closed-loop control in the controller, and the output drive signal controls the first switching transistor (S). a Second switch S b Third switch S c and the fourth open pipe S d On / off.

[0015] Preferably, based on harmonic amplitude Ihar Harmonic frequency f har The amplitude U of the suppressed harmonic modulation voltage is obtained. har The details are as follows:

[0016] U har =2πf har L r I har

[0017] Among them, f har Indicates harmonic frequency; L r Indicates resonant inductance; I har Harmonic amplitude.

[0018] Preferably, the normalized harmonic current is fed into an integration delay stage to obtain the frequency and phase of the suppressed harmonic modulation voltage, and the amplitude U of the harmonic modulation voltage. har The combination yields a harmonic-suppressed modulation voltage, as detailed below:

[0019]

[0020] Among them, u har Indicates the voltage for suppressing harmonic modulation; f har Represents harmonic frequency; θ har Indicates the harmonic phase.

[0021] Preferably, the harmonic suppression modulation voltage is compared with the AC power supply voltage u. s By superimposing the results, the output capacitance C is obtained. r Reference voltage u cr-ref The details are as follows:

[0022]

[0023] Preferably, the first switching transistor S is controlled. a and the fourth open pipe S d The drive signal is the same, controlling the second switch S b and the third switch S c The drive signals are the same, and control the first switching transistor S. a and the fourth open pipe S d The drive signal and control of the second switch S b and the third gate S c The driving signal is opposite.

[0024] The beneficial effects of this invention are as follows:

[0025] (1) The fractional-order filter of the present invention is composed of a controllable fractional-order capacitor and an inductor connected in series, connected between the AC bus and ground, and in parallel with the load; the fractional-order filter can realize the function of controllable center frequency and Q value; by controlling the output voltage u of the fractional-order circuit. cr Indirectly control the resonant inductor L r The voltage causes the center frequency of the fractional-order filter to lock at the harmonic frequency point; the energy storage capacitor C d It is used for periodically absorbing and releasing reactive power and compensating for power dissipated on the actual equivalent series resistance, utilizing capacitor C. d The energy makes the port output resistance negative, allowing the impedance phase angle of the filter to be adjusted at a specific frequency, adaptively suppressing current harmonics with random fluctuations in frequency and amplitude;

[0026] (2) The present invention is not sensitive to device parameters; on the one hand, it can maintain good harmonic suppression capability within a certain parameter offset; on the other hand, it can suppress harmonic currents within a certain harmonic frequency offset.

[0027] (3) The controllable fractional-order capacitor circuit of the present invention can change the equivalent capacitance and equivalent resistance of the port, exhibiting negative resistance characteristics in the output impedance of the port, and adjusting the minimum resonant equivalent resistance. Attached Figure Description

[0028] Figure 1 The circuit diagram of the adaptive AC fractional-order filter according to an embodiment of the present invention is shown below.

[0029] Figure 2 This is a modal analysis diagram of the controllable fractional-order capacitor circuit according to an embodiment of the present invention; wherein, (a) represents mode I, and i Lf >0; (b) represents mode II, and i Lf >0; (c) represents mode I, and i Lf <0; (d) represents mode II, and i Lf <0;

[0030] Figure 3 This is a control block diagram of the adaptive AC fractional-order filter according to an embodiment of the present invention;

[0031] Figure 4 These are the simulation waveforms and Fourier analysis diagrams of the load current for an LC series filter under ideal conditions; where (a) represents the simulation waveform and (b) represents the Fourier analysis diagram of the load current.

[0032] Figure 5 These are the simulation waveforms and Fourier analysis diagrams of the LC series filter with a capacitance error of 25%; where (a) represents the simulation waveform and (b) represents the Fourier analysis diagram of the load current.

[0033] Figure 6 These are simulation waveforms and Fourier analysis diagrams of the load current for harmonic suppression according to an embodiment of the present invention; wherein, (a) represents the simulation waveform and (b) represents the Fourier analysis diagram of the load current.

[0034] Among them, u s The phase voltage of the AC bus; i bus For AC bus phase current; i har For harmonic absorption branch current; i o i is the load current; Lf For the output inductor current; u o The load voltage; u cr The output capacitor voltage; u cd C is the voltage of the energy storage capacitor; r For output capacitor; L f For output inductance; L r For resonant inductance; r req For controllable equivalent series resistance; C d For energy storage capacitors; S a For the first switch; S b For the second switch; S c For the third switch; S d For the fourth switch; R o For load; I har f is the harmonic amplitude; har For the harmonic frequency, θ har This is the harmonic phase. Detailed Implementation

[0035] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0036] In the description of this invention, it should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0037] The adaptive AC fractional-order filter of the present invention, by constructing the controllable fractional-order capacitor circuit, adaptively adjusts the Q value of the filter to achieve an extremely low equivalent impedance to harmonic currents of different frequencies, thereby suppressing current harmonics with random fluctuations in frequency and amplitude.

[0038] See Figure 1 As shown in the figure, this embodiment of an adaptive AC fractional-order filter includes: a controllable fractional-order capacitor and a harmonic inductor L connected in series. rThe fractional-order filter is connected between the AC bus and ground, and to the load R. o They are connected in parallel;

[0039] The controllable fractional-order capacitor includes an output capacitor C. r Output inductor L f First switching transistor S a Second switch S b Third switch S c Fourth open valve S d and an energy storage capacitor C d Composition; the first switching transistor S a With the second switching transistor S b The third switch S is connected in series. c With the fourth switch S d They are connected in series and in parallel to the energy storage capacitor C. d Both ends; the third switch S c With the fourth switch S d The connection point is connected via the output inductor L f Connected to output capacitor C r At one end, the first switch S a With the second switching transistor S b The connection point is directly connected to capacitor C. r The other end.

[0040] The controllable fractional-order capacitor circuit used can utilize harmonic energy to assist in power supply. It can not only change the equivalent capacitance of the port, but also adjust the equivalent resistance, and even exhibit negative resistance characteristics, thereby adjusting the minimum resonant equivalent resistance of the harmonic suppression branch.

[0041] To suppress harmonic frequencies of f har harmonic current i har As long as the output capacitor voltage u is controlled cr The frequency in contains f har And its phase lags the harmonic current i har A quarter of a cycle

[0042] Let the harmonic current i har The expression is:

[0043] i har =I har sin(2πf har t+θ har (1)

[0044] Among them, I har f har θ har They are i harThe amplitude, frequency, and phase of the harmonic current i. har All of it is absorbed by the fractional-order filter, and the harmonic current i generated on the equivalent resonant capacitor har With the suppression of harmonic modulation voltage u har The relationship is as follows:

[0045]

[0046] The harmonic modulation voltage u can be obtained. har The expression is shown in formula (3).

[0047]

[0048] Among them, C eq The equivalent resonant capacitance value is determined by the harmonic current frequency, indicating that it satisfies the condition at the harmonic frequency f. har With inductor L r The capacitance C that produces the series resonance condition. eq The expression is

[0049]

[0050] From (3) and (4), we can obtain the voltage u. har The expression is as follows:

[0051]

[0052] Among them, U har This indicates the amplitude of the voltage used to suppress harmonic modulation.

[0053] The reference voltage u of the output capacitor cr-ref For voltage u har With AC bus voltage u s The sum of the reference voltage u cr-ref It is expressed as follows:

[0054]

[0055] The quality factor Q of the equivalent series resonance can be obtained as follows:

[0056]

[0057] As can be seen from equation (7), the quality factor Q is related to the equivalent resistance r. req The quantitative relationship is determined by control. Traditional LC series resonance calculates the quality factor Q and resonant voltage using the minimum line impedance; therefore, an excessively small minimum line impedance leads to an excessively high resonant voltage. However, the adaptive fractional-order filter of this invention first determines the resonant voltage amplitude, and then uses the voltage amplitude to deduce the minimum line impedance and quality factor Q. This avoids the occurrence of extremely small equivalent resistance r.req Overvoltage caused capacitor C to break down r The situation.

[0058] See Figure 2 As shown, the controllable fractional-order capacitor circuit can be divided into two operating modes depending on the on / off state of the switching transistor. The switching transistor S... a With S d As a group, the switching transistor S b With S c The two sets of switches are complementary and conduction is achieved as one group.

[0059] Mode I: Switch S a S d Turn on, switch S b S c Turn off. When the output inductor L f Current i Lf When the direction is positive, such as Figure 2 As shown in (a), the output inductor current i Lf Through the switching transistor S a S d The body diode also serves as the output capacitor C. f and energy storage capacitor C d Charging, output inductor current i Lr The positive direction decreases, and the output capacitor voltage u cr The voltage u of the energy storage capacitor increases. cd Rise; when the output inductance L f Current i Lf When the direction is negative, such as Figure 2 As shown in (c), the output inductor current i Lf Through the switching transistor S a S d At the same time, it is the output capacitor C f and energy storage capacitor C d Release energy and output inductor current i Lr Reverse increase, output capacitor voltage u cr The voltage of the energy storage capacitor, u, decreases. cd decline.

[0060] Mode II: Switch S a S d Turn off, lower switch S b S c Turn on. When the output inductor L f Current i Lf When the direction is positive, such as Figure 2 As shown in (b), the output inductor current i Lf Through the switching transistor S c S d , is the output capacitor C fCharging is performed on the energy storage capacitor C. d Release energy and output inductor current i Lr As the positive voltage increases, the output capacitor voltage u cr The voltage u of the energy storage capacitor increases. cd Decrease; when the output inductance L f Current i Lf When the direction is negative, such as Figure 2 As shown in (d), the output inductor current i Lf Through the switching transistor S a S d The body diode is the output capacitor C. f Release energy for the energy storage capacitor C d Charging, output inductor current i Lr The reverse decreases, and the output capacitor voltage u cr The voltage u of the energy storage capacitor increases. cd decline.

[0061] It should be noted that, Figure 2 In the middle, when S a and S d Activation, S b and S c When turned off, the current i Lf There is always a tendency to decrease in the positive direction (both positive decrease and negative increase are the same trend). When the circuit is operating normally, if the current is 0, then only switch S needs to be turned on. b S c This will make the current i Lf The direction is positive; if the current magnitude is negative at this time, then in the subsequent switching cycles, S will be positive. b S c The duty cycle is greater than 0.5, and the current i Lf The direction will eventually be right.

[0062] See Figure 3 As shown, in this embodiment, the control process of the adaptive AC fractional-order filter is as follows. First, the bus current i... bus By performing harmonic detection and separating the fundamental current from the harmonic current, the harmonic amplitude I can be obtained. har Harmonic frequency f har With harmonic phase θ har Using harmonic amplitude I har Harmonic frequency f har The amplitude U of the harmonic modulation voltage can be obtained using formulas (3) and (4). har By using the normalized harmonic current into the integral delay stage, the frequency and phase of the harmonic-modulated voltage can be obtained. Then, by superimposing the AC power supply voltage u... s The output capacitor C of the fractional-order circuit is obtained.r Reference voltage u cr-ref Finally, the reference voltage u cr-ref The difference between the output capacitor voltage (ucr) and the input voltage (μr) is subtracted and fed into a proportional-integral (PI) controller for closed-loop voltage control, which controls the switching transistor S. a S b S c S d The switch. Specifically, when the PI output is greater than the PWM carrier wave, S... b and S c Turn on; when the PI output is less than the PWM carrier wave, S a and S d Conduction. Figure 3 In the middle, d sa d sb d sc and d sd These are drive signals, used to drive the switching transistors S in the main circuit. a S b S c and S d .

[0063] This only applies to the output capacitor C. r Perform voltage closed-loop control, without affecting the energy storage capacitor C. d Voltage closed-loop control is performed because when the output capacitor C is... r Viewed as an AC source, the four switching transistors S a S b S c and S d The body diode to the energy storage capacitor C d In passive rectification, the fundamental frequency and excess harmonic energy on the AC bus will contribute to the energy storage capacitor C. d Charge the capacitor to maintain its voltage u. cd Relative stability within a cycle.

[0064] In the energy storage capacitor C d In this process, the energy used to suppress harmonics can be drawn from the harmonics themselves, because from a power perspective, the energy of the harmonic peaks can be filled into the troughs. The fundamental wave provides C... d The electrical energy generated is mainly used to offset line losses and switching losses.

[0065] To verify the feasibility of the method, circuit simulation was performed on the method proposed in this invention, and the specific circuit parameters are shown in the table.

[0066]

[0067] First, harmonic suppression simulation is performed using only a traditional LC series filter. When the resonant inductor L...r =2.5mH ​​and resonant capacitance C r =40.5uF has no error, and its resonant frequency is 500Hz. If there is a 15% tenth harmonic current with the fundamental frequency (50Hz) in the AC bus, a numerically accurate resonant inductor L should be used. r With resonant capacitor C r For harmonic suppression, see the simulation waveform. Figure 4 As shown. Load current i o In the Fourier analysis, the amplitude of the fundamental frequency current is 7.76A, and the amplitude of the residual tenth harmonic is 0.10A, accounting for only 1.29% of the fundamental frequency component, and the THD of this current is only 1.83%. However, in practical applications, it is difficult to achieve such good results, especially when the value of the resonant capacitor is accurate to three significant digits.

[0068] Secondly, when using resonant inductor L r =2.5mH ​​and resonant capacitance C r When using a 30uF capacitor for harmonic suppression, the resonant frequency has shifted to 581Hz due to a 25% capacitance error. If a 10th harmonic current with a fundamental current amplitude of 15% exists in the AC bus, the aforementioned resonant inductor L... r With resonant capacitor C r For harmonic suppression, see the simulation waveform. Figure 5 As shown. At this time, the resonant inductor L... r With resonant capacitor C r The resonant frequency is no longer equal to the harmonic frequency, and this LC series filter has a significant equivalent impedance to the harmonic current. At this time, the load current i... o In the Fourier analysis, the amplitude of the fundamental frequency current is 7.75A, and the amplitude of the residual tenth harmonic is 4.05A, accounting for 52.26% of the fundamental frequency component. Therefore, when the resonant frequency does not match the frequency of the harmonic to be suppressed, it will not only fail to effectively suppress the harmonic current, but will also deteriorate the power quality and even increase the risk of device damage.

[0069] Finally, the resonant inductor L is used again. r =2.5mH ​​and resonant capacitance C r =30uF for suppressing 500Hz harmonic current, but at this time, the application Figure 1 The fractional-order capacitor circuit shown above relates to the resonant capacitor C. r Capacitance compensation and resonant voltage peak adjustment were performed. Although the natural resonant frequency of the resonant inductor and capacitor had shifted to 581Hz, after compensation by the fractional-order capacitor circuit, the simulation waveform is shown below. Figure 6 As shown. Energy storage capacitor voltage u cdAlthough the oscillation amplitude is large within one power frequency cycle, it can still maintain a relatively stable voltage. Under steady state, the voltage at the beginning and end of each cycle is equal; resonant capacitor C r The voltage is a sinusoidal voltage superimposed on the fundamental voltage and a harmonic frequency, and its amplitude and phase are consistent with those of an error-free LC series filter under ideal conditions; the load current i o There is no obvious tenth harmonic residue, only a small distortion near zero. Load current i o In the Fourier analysis, the amplitude of the fundamental frequency current is 7.75A, and the amplitude of the residual tenth harmonic is 0.09A, accounting for 1.16% of the fundamental frequency component. This is even slightly lower than that of an error-free LC series filter under ideal conditions. However, the harmonic components of other frequencies increase slightly, with a THD of 2.7%. It can be seen that the LC series filter with fractional-order capacitor circuit compensation effectively absorbs the harmonic current and has adaptive properties.

[0070] The above is only one specific embodiment of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing the protection scope of the present invention.

Claims

1. An adaptive AC fractional-order filter, characterized in that, include: Series-connected controllable fractional capacitor and harmonic inductor L r The fractional-order filter is connected between the AC bus and ground, and to the load R. o They are connected in parallel; The controllable fractional-order capacitor includes an output capacitor C. r Output inductor L f First switching transistor S a Second switch S b Third switch S c Fourth open valve S d and an energy storage capacitor C d Composition; the first switching transistor S a With the second switching transistor S b The third switch S is connected in series. c With the fourth switch S d They are connected in series and in parallel to the energy storage capacitor C. d Both ends; the third switch S c With the fourth switch S d The connection point is connected via the output inductor L f Connected to output capacitor C r At one end, the first switch S a With the second switching transistor S b The connection point is directly connected to capacitor C. r The other end; The voltage of the controllable fractional capacitor is controlled by a closed-loop voltage control, as follows; For bus current i bus Harmonic detection is performed to separate the fundamental current and harmonic currents, and the harmonic amplitude I at this time is obtained. har Harmonic frequency f har With harmonic phase θ har ; Based on harmonic amplitude I har Harmonic frequency f har The amplitude U of the suppressed harmonic modulation voltage is obtained. har ; The normalized harmonic current is fed into an integration delay stage to obtain the frequency and phase of the suppressed harmonic modulation voltage, and the amplitude U of the harmonic modulation voltage. har Combined, a harmonic modulation voltage is obtained; The harmonic modulation voltage and AC power supply voltage u will be suppressed. s The output capacitor C is obtained by superimposing the results. r Reference voltage u cr-ref ; Reference voltage u cr-ref The difference between the output capacitor voltage (ucr) and the output capacitor voltage (ucr) is used to perform voltage closed-loop control in the controller, and the output drive signal controls the first switching transistor (S). a Second switch S b Third switch S c and the fourth open pipe S d On / off.

2. The adaptive AC fractional-order filter according to claim 1, characterized in that, Based on harmonic amplitude I har Harmonic frequency f har The amplitude U of the suppressed harmonic modulation voltage is obtained. har The details are as follows: U har = 2πf har L r I har Among them, f har Indicates harmonic frequency; L r Indicates resonant inductance; I har Harmonic amplitude.

3. The adaptive AC fractional-order filter according to claim 1, characterized in that, The normalized harmonic current is fed into an integration delay stage to obtain the frequency and phase of the suppressed harmonic modulation voltage, and the amplitude U of the harmonic modulation voltage. har The combination yields a harmonic-suppressed modulation voltage, as detailed below: Among them, u har Indicates the voltage for suppressing harmonic modulation; f har Represents harmonic frequency; θ har Indicates the harmonic phase.

4. The adaptive AC fractional-order filter according to claim 3, characterized in that, The harmonic modulation voltage and AC power supply voltage u will be suppressed. s The output capacitor C is obtained by superimposing the results. r Reference voltage u cr-ref The details are as follows:

5. The adaptive AC fractional-order filter according to claim 1, characterized in that, Control the first switch S a and the fourth open pipe S d The drive signal is the same, controlling the second switch S b and the third switch S c The drive signals are the same, and control the first switching transistor S. a and the fourth open pipe S d The drive signal and control of the second switch S b and the third gate S c The driving signal is opposite.

Images