A High-Power Filter and Control Method Based on the Parallel Connection of Fractional-Order Positive and Negative Inductors

Abstract

The present invention provides a high-power filter based on the parallel connection of fractional-order positive and negative inductors and a control method. The filter includes a fractional-order negative inductor #imgabs0# and a positive inductor #imgabs1#, which are in a parallel relationship. The fractional-order negative inductor #imgabs2# includes a first switching tube V1, a second switching tube V2, a third switching tube V3, a fourth switching tube V4, filter inductors L1 and L2, a filter capacitor C f , a filter damping R f , a grounding capacitor C g , a sampling resistor R, a DC-DC conversion circuit, a self-power supply module, an MCU controller, a digital-to-analog converter AD, and a sine pulse width modulation module SPWM. By changing the parameters of the MCU controller in the solution of the present invention, the inductance value and order of the fractional-order inductor can be arbitrarily changed, so as to change the inductance value of the high-power filter with the parallel connection of fractional-order positive and negative inductors, realizing the low cost, small volume, high power density of the filter inductor, and the flexibility of adjustable order and inductance value. It can be applied to high-power scenarios with high harmonic content and achieve better filtering effects.

Description

Technical Field

[0001] The present invention relates to the technical field of power electronic converter control and current harmonic suppression, and particularly to a high-power filter based on parallel connection of fractional-order positive and negative inductors and a control method therefor. Background Art

[0002] In recent years, due to the inherent flexibility of differentiation and integration, fractional calculus has been successfully applied in fields such as control systems, model identification, and circuit systems. Existing research results show that many physical phenomena in nature are essentially fractional-order in nature. For example, inductors and capacitors are actually fractional-order components. The model obtained by modeling an inductor with fractional calculus theory is not only more accurate but also more complete compared with the integer-order model. In addition, after modeling the inductor with fractional calculus, any order can be set, so that more functions can be realized with more degrees of freedom and a wider range of application scenarios can be applied.

[0003] As the most basic unit of a fractional-order circuit system, the construction of the topological structure of a fractional-order inductor and the implementation of a control method are the basis for studying fractional-order circuit systems. Currently, the construction methods of fractional-order inductors are mainly divided into two types: single-component construction methods and multi-component construction methods.

[0004] The single-component construction method, that is, manufacturing a fractional-order inductor through a process, mainly uses electrode surface areas with different fractal structures, highly conductive materials with different electrolytes, etc. In this implementation method, once the device is encapsulated, the order and inductive reactance value of the single-component fractional-order inductor are fixed. When it is necessary to change the order and inductive reactance of the inductor, it is necessary to redesign and manufacture. Moreover, this method can only realize fractional-order inductors with an order less than 1, and the application scenario is very limited.

[0005] The multi-component construction method consists of passive devices such as resistors and capacitors, as well as active devices such as operational amplifiers and power electronic switch elements. It is mainly divided into three categories: multi-component fractional-order elements based on passive devices, multi-component fractional-order elements based on operational amplifiers, and multi-component fractional-order elements based on power electronic converters. For the multi-component fractional-order elements based on passive devices and those based on operational amplifiers, these two methods use a large number of components, the circuit structure is very complex, and the order and inductance value of the fractional-order inductor are fixed. When the order and inductance value need to be changed, the entire circuit structure needs to be replaced, which is inefficient and costly. At the same time, the use of analog devices such as operational amplifiers limits the circuit model to low-power scenarios in the milliwatt level, restricting its application in the electrical field. The multi-component fractional-order element based on power electronic converters essentially realizes the fractional-order inductor through control. Therefore, this method can flexibly change the order and inductive reactance characteristics of the fractional-order inductor by changing the parameters of the controller, and can be applied to various power scenarios, having broad application prospects. However, most of the currently mature power electronic converter-based solutions exhibit the characteristics of fractional-order inductors only for specific frequencies and cannot be applied to filter circuits.

[0006] Inductors are widely used in power systems. However, the current application of traditional inductors has problems such as large volume, low power density, and high cost. And during use, as traditional inductors age and degenerate, their device parameters change. Once put into use, they cannot be adjusted in real time, and their applicability to load and frequency fluctuations is poor, resulting in a decline in filtering quality. Summary of the Invention

[0007] In view of the above problems, the present invention proposes a high-power filter and control method based on the parallel connection of fractional-order positive and negative inductors. By connecting the positive inductor and the negative inductor in parallel, the overall inductance value is increased, thereby achieving a better filtering effect. This filter can achieve adjustable order and inductance value of the inductor under different frequencies, solving the problems of increased volume, complex design, non-arbitrary adjustment of order and inductance value, and limited application power level brought about by the method of using passive components to construct fractional-order inductors. At the same time, this control method exhibits the inductive reactance characteristics of the inductor in the full frequency band, so it can be applied to filter circuits.

[0008] On the one hand, the present invention proposes a high-power filter based on the parallel connection of fractional-order positive and negative inductors, including a fractional-order negative inductor and a positive inductor , and the two are in a parallel relationship. The positive inductor is a conventional physical inductor, and the fractional-order negative inductor is equivalent to a circuit composed of power components and can exhibit the properties of a fractional-order negative inductor.

[0009] Fractional-order negative inductor Specifically include: the first switching transistor V 1 , the second switching transistor V 2 , the third switching transistor V 3 , the fourth switching transistor V 4 , the filter inductors L 1 and L 2 , the filter capacitor C f , the filter damping resistor R f , the grounding capacitor C g , the sampling resistor R, the DC-DC conversion circuit, the self-power supply module, the Microcontroller Unit (MCU) controller, the analog-to-digital converter AD, and the sine pulse width modulation module SPWM. All the switching transistors are insulated gate bipolar transistors IGBTs.

[0010] The two output terminals of the DC-DC conversion circuit, that is, the DC chopper circuit, are respectively connected to the collector of the first switching transistor V 1 and the emitter of the third switching transistor V 3 . The first switching transistor V 1 and the third switching transistor V 3 are in series. The second switching transistor V 2 and the fourth switching transistor V 4 are in series. The collector of the second switching transistor V 2 is connected to one output terminal of the DC-DC conversion circuit, and the emitter of the fourth switching transistor V 4 is connected to the other output terminal of the DC-DC conversion circuit. The emitter of the first switching transistor V 1 is connected to the collector of the third switching transistor V 3 . The collector of the first switching transistor V 1 is connected to the collector of the second switching transistor V 2 . The emitter of the second switching transistor V 2 is connected to the collector of the fourth switching transistor V 4 . The emitter of the third switching transistor V 3 is connected to the emitter of the fourth switching transistor V 4 . The gates of the four switching transistors are connected to the gate drive control signals. Power diodes are connected in parallel across both ends of the four switching transistors. The collector of each switching transistor is connected to the negative electrode of the diode, and the emitter of each switching transistor is connected to the positive electrode of the diode;

[0011] The four switching transistors form a single-phase inverter. When working normally, the control signal controls the first state where the switching transistors V 1 and V 4 are conducting simultaneously, and the switching transistors V 2 and V 3 are turned off. The second state is where the switching transistors V 1 and V 4 are turned off, and the switching transistor V 2And the switch tube V 3 They are turned on at the same time, and the two states alternate cyclically, so that the excitation voltage and port current at both ends of ports A and B conform to the characteristics of fractional-order negative inductance.

[0012] Filter inductor L 1 and L 2 、Filter capacitor C f and filter damping R f Constitute LLC filter circuit, filter damping R f Connected in series with the filter capacitor, the LLC filter circuit is considered as a whole, responsible for filtering out the harmonics introduced by the switch tube, where the filter inductor L 1 One end is connected to the second switch tube V 2 The emitter, filter inductor L 1 The other end is connected to the filter inductor L 2 And filter capacitor C f One end of the filter inductor L 2 The other end of the sampling resistor R is connected to one end of the sampling resistor R, and the other end of the sampling resistor R is connected to an AD digital-to-analog converter, which is used to convert the current between the A and B ports Converted into digital signal, another AD digital-to-analog converter converts the analog voltage signal between A and B ports into digital signal, which is convenient for the MCU controller to process later. f The other end of the filter damping R f Connected, filter damping R f The other end is connected to the third switch tube V 3 The collector, grounded capacitor C g One end of the filter damping R f The other end of the capacitor C is connected to ground g The other end of the sampling resistor R is grounded, port A is the other end of the sampling resistor R, and port B is the filter damping R in the LLC filter circuit. f At the other end, the output voltage of the single-phase inverter contains more harmonics. The LLC filter circuit is used to filter out these harmonic signals and improve the output power quality.

[0013] The self-powered module obtains power directly from the drain-source end of the switch tube element, charges the capacitor in the self-powered module to store energy, and supplies power to the gate drive circuit of the switch element and the MCU controller. The DC-DC conversion circuit takes power from the DC side bus to obtain the DC voltage U required by the single-phase full-controlled bridge. DC .

[0014] The MCU controller applies the excitation voltage u to the ports A and B of the fractional-order negative inductor. g (t) and the port current i L(t) Sampling is performed to generate a control signal wave for the switching tube in the fractional-order negative inductor circuit.

[0015] The sine pulse width modulation module SPWM modulates the control signal wave output by the MCU controller using a triangular carrier wave to generate a control signal for controlling the switching tube.

[0016] On the other hand, the present invention provides a control method for a high-power filter based on the parallel connection of fractional-order positive and negative inductors. The method includes the following steps:

[0017] Step S1: Determine the value of the filtering inductor according to the power quality requirements of grid connection, and then calculate the inductance values of the fractional-order negative inductor and the positive inductor ;

[0018] Step S2: Calculate the order of the fractional-order positive inductor based on the voltage and current in the fractional-order positive inductor, and set the order of the negative inductor equal to the order of the positive inductor to obtain the control parameters of the MCU;

[0019] Step S3: Obtain the voltage of the external excitation at both ends of ports A and B of the fractional-order negative inductor and the port current , and set the internal parameter auxiliary resistance of the fractional-order negative inductor and the output voltage of the DC-DC conversion circuit, and generate a gate drive control signal according to the control strategy;

[0020] Step S4: Check whether the filtering result of the positive and negative inductor parallel filter meets the power quality requirements, and further adjust the positive and negative inductor parameters.

[0021] Further, the specific content of step S1 includes:

[0022] According to the power quality requirements of grid connection, determine the value of the filtering inductor , and then calculate the inductance values of the fractional-order negative inductor and the positive inductor . When the inductors are connected in parallel, the equivalent filtering inductor value and the fractional-order negative inductor , the positive inductor have the following relationship: , where is the inductance value of the fractional-order negative inductor, is the inductance value of the fractional-order positive inductor. When the magnitude of tends to , the equivalent inductor after parallel connection is equivalent to a very large inductor in the full frequency band. Such a very large equivalent inductor It can replace the traditional large inductor for filtering, and the inductance values ​​of the negative inductor and the positive inductor can be determined according to actual needs.

[0023] Furthermore, the step S2 specifically includes:

[0024] According to the value of fractional negative inductance And the inductance of fractional positive inductance Calculate the inductive reactance of positive and negative inductors in parallel for:

[0025]

[0026] in, is the order of the fractional positive inductance, is the order of the fractional negative inductance, , is the fundamental angular frequency of the excitation voltage across the parallel structure, is the fundamental frequency;

[0027] The voltage-current relationship for a positive inductor is as follows: ,in, is the voltage applied to the positive inductor, is the current in the positive inductor;

[0028] Performing Fourier transform on the voltage-current relationship of positive inductance yields the following relationship:

[0029]

[0030] Taking the logarithm of both sides of the equation, we get the following expression:

[0031]

[0032] According to the above formula, the order of positive inductance is obtained , and set the order of the negative inductance to be equal to the order of the positive inductance, and finally adjust the equivalent inductance of the fractional-order negative inductance so that the overall inductance after parallel connection meets the required inductance.

[0033] Furthermore, the step S3 specifically includes:

[0034] Step S31: Auxiliary resistance in fractional-order negative inductance and the output voltage of the DC-DC converter circuit Satisfies the following relationship:

[0035]

[0036] in, The triangle carrier amplitude used by the sine pulse width modulation module SPWM, , is the amplitude of the external excitation voltage, is the fundamental angular frequency of the external excitation voltage signal, and the voltage proportionality coefficient ;

[0037] Step S32: In each sampling period, the voltage of the external excitation across both ends of the fractional-order negative inductor port and the port current are sampled, and the sampling results are input into the MCU controller;

[0038] Step S33: Generate the signal wave of bipolar modulation in the fractional-order negative inductor topology. Without considering the influence of the LLC filter circuit, the mathematical model of the fractional-order negative inductor is expressed as follows:

[0039]

[0040] where β is the order of the fractional-order negative inductor, is the inductance value of the fractional-order negative inductor, is the excitation voltage across both ends of the fractional-order negative inductor port in the frequency domain representation, is the port current in the frequency domain representation;

[0041] There is the following relationship between the external excitation voltage and the port current of the fractional-order negative inductor and both sides of the sampling resistor:

[0042]

[0043] where, is the filtered voltage signal, R is the sampling resistor, is the fractional-order differential operator;

[0044] After simplification, we get:

[0045]

[0046] Since the output of the inverter and the modulation signal have the same phase and are proportional in amplitude, the signal wave of the MCU controller is:

[0047]

[0048] where the voltage proportionality coefficient , is the amplitude of the triangular carrier wave, is the output DC voltage of the DC-DC conversion circuit, is the fractional-order integral operator, and are reciprocals of each other.

[0049] Taking into account the filtering inductor in the LLC filter circuit and the filtering capacitor as well, the parameters of each component in the fractional-order negative inductor circuit have the following relationships: Among them,

[0050]

[0051] where is the voltage of the filtering capacitor branch, is the current of the filtering capacitor branch, is the current flowing through the filtering inductor , is the output voltage of the single-phase inverter, that is, the voltage between the emitter of the second switching tube V2 and the collector of the third switching tube V3;

[0052] Therefore, the signal wave of the MCU controller considering the influence of the LLC filter circuit is obtained as follows:

[0053]

[0054] where:

[0055]

[0056] The generation methods of these two signal waves can be determined according to the actual application situation.

[0057] Step S34: The sine pulse width modulation module SPWM performs sine pulse width modulation on the signal wave and the local triangular carrier wave to generate control signals for the four switching devices.

[0058] The present invention has the following beneficial technical effects:

[0059] A high-power filter and control method based on parallel connection of fractional-order positive and negative inductors proposed by the present invention can arbitrarily change the inductance value and order of the fractional-order inductor by changing the parameters of the MCU controller, that is, the inductance value and order of the fractional-order negative inductor, overcoming the disadvantages of the traditional fractional-order inductor design method, such as complex circuit structure, high cost, and fixed and unchangeable order and inductance value;

[0060] The solution of the present invention has a large adjustment flexibility in the inductor value and order of the filter, and can be adjusted according to the requirements of grid-connected power quality, changes in load and frequency, and changes in equipment parameters to ensure consistent filtering and suppression performance under different working conditions and improve the robustness of the system;

[0061] The solution of the present invention connects a positive inductor and a negative inductor in parallel, significantly increasing the overall inductive reactance, thus achieving a better filtering effect. On the premise of achieving the same filtering effect, the volume of the physical inductor can be reduced, thereby improving the power density and saving costs;

[0062] The power rating of the filter according to the solution of the present invention can be determined according to the actual application scenario, so it can be applied to high-power power transmission networks;

[0063] Since the high-power filter of the present invention has a parallel structure, it is convenient to improve the inductors that have been put into use. On the basis of the inductors that have been put into use, an H-bridge equivalent structure of a full-band fractional-order negative inductor is connected in parallel to increase the inductance value, thereby achieving a larger inductive reactance and a better filtering effect;

[0064] The solution of the present invention approximates the fractional-order integral operator through an Oustaloup filter. Users can select the frequency band according to actual needs to achieve the response of the full frequency band, so that the fractional-order negative inductor in the present invention exhibits the inductive reactance characteristics of the fractional-order negative inductor in the full frequency band and is suitable for scenarios with a high harmonic content. Description of the Drawings

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0066] Figure 1 It is a schematic diagram of the overall structure of a high-power filter based on the parallel connection of fractional-order positive and negative inductors provided by an embodiment of the present invention;

[0067] Figure 2 It is a schematic diagram of the specific structure of the fractional-order negative inductor provided by an embodiment of the present invention;

[0068] Figure 3 It is a schematic diagram of the flow of a control method for a high-power filter based on the parallel connection of fractional-order positive and negative inductors provided by an embodiment of the present invention;

[0069] Figure 4 It is a system block diagram of a control method for a fractional-order negative inductor that ignores the influence of the filtering circuit provided by an embodiment of the present invention;

[0070] Figure 5 It is a schematic diagram of the piecewise linear approximation of the Oustaloup filter provided by an embodiment of the present invention;

[0071] Figure 6It is the system block diagram of the control method of the fractional-order negative inductor considering the influence of the filter circuit provided by the embodiment of the present invention;

[0072] Figure 7 It is the schematic diagram of the DC component extraction and elimination of the Oustaloup filter provided by the embodiment of the present invention;

[0073] Figure 8 It is the simulation verification result of the 1st-order fractional-order negative inductor under 50Hz excitation provided by the embodiment of the present invention;

[0074] Figure 9 It is the simulation verification result of the 1st-order fractional-order negative inductor under 100Hz excitation provided by the embodiment of the present invention;

[0075] Figure 10 It is the simulation verification result of the 1st-order fractional-order negative inductor under 300Hz excitation provided by the embodiment of the present invention;

[0076] Figure 11 It is the simulation verification result of the 0.9th-order fractional-order negative inductor under 100Hz excitation provided by the embodiment of the present invention;

[0077] Figure 12 It is the simulation verification result of the 1.1th-order fractional-order negative inductor under 100Hz excitation provided by the embodiment of the present invention;

[0078] Figure 13 It is the filtering effect diagram of the full-band fractional-order negative inductor under multiple harmonic scenarios provided by the embodiment of the present invention;

[0079] Figure 14 It is the measurement result of the harmonic content before filtering provided by the embodiment of the present invention;

[0080] Figure 15 It is the measurement result of the harmonic content after filtering provided by the embodiment of the present invention;

[0081] Figure 16 It is the effect diagram of the increase in the inductive reactance of the high-power filter with the parallel connection of 0.4mH positive inductor and 0.5mH negative inductor provided by the embodiment of the present invention;

[0082] Figure 17 It is the effect diagram of the increase in the inductive reactance of the high-power filter with the parallel connection of 0.4mH positive inductor and 0.4mH negative inductor provided by the embodiment of the present invention. Specific embodiments

[0083] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0084] The present invention provides a high-power filter and a control method based on the parallel connection of fractional-order positive and negative inductors. The overall structure of the high-power filter is as Figure 1 shown, between port A 0 and port B 0 is a high-power filter based on the parallel connection of fractional-order positive and negative inductors proposed by the present invention, including a fractional-order negative inductor and a positive inductor , the two are in a parallel relationship, and can realize the high-power full-band filtering function and increase the inductive reactance.

[0085] Figure 2 is a schematic structural diagram of the fractional-order negative inductor . The H-bridge equivalent topology structure of the fractional-order negative inductor includes: the first switch tube V 1 , the second switch tube V 2 , the third switch tube V 3 , the fourth switch tube V 4 , filter inductors L 1 and L 2 , filter capacitor C f , filter damping R f , grounding capacitor C g , sampling resistor R, DC-DC conversion circuit, self-power supply module, Microcontroller Unit (MCU) controller, digital-to-analog converter AD and sine pulse width modulation module SPWM. All switch tubes are insulated gate bipolar transistors IGBTs.

[0086] The two output terminals of the DC-DC conversion circuit, that is, the DC chopper circuit, are respectively connected to the collector of the first switch tube V 1 and the emitter of the third switch tube V 3 . The first switch tube V 1 and the third switch tube V 3 are in series. The second switch tube V 2 and the fourth switch tube V 4 are in series. The collector of the second switch tube V 2 is connected to one output terminal of the DC-DC conversion circuit, and the emitter of the fourth switch tube V 4 is connected to the other output terminal of the DC-DC conversion circuit. The collector of the first switch tube V 1The emitter is connected to the third switching transistor V 3 's collector, and the collector of the first switching transistor V 1 is connected to the collector of the second switching transistor V 2 's collector, and the emitter of the second switching transistor V 2 is connected to the collector of the fourth switching transistor V 4 's collector, and the emitter of the third switching transistor V 3 is connected to the emitter of the fourth switching transistor V 4 's emitter. The gates of the four switching transistors are connected to the gate drive control signal. Power diodes are connected in parallel across both ends of the four switching transistors. The collector of each switching transistor is connected to the negative pole of the diode, and the emitter of each switching transistor is connected to the positive pole of the diode;

[0087] The four switching transistors form a single-phase inverter. During normal operation, the control signal controls the first state where switching transistors V 1 and V 4 conduct simultaneously, and switching transistors V 2 and V 3 are turned off. The second state is where switching transistors V 1 and V 4 are turned off, and switching transistors V 2 and V 3 conduct simultaneously. The two states alternate cyclically, making the excitation voltage and port current at both ends of ports A and B conform to the characteristics of a fractional-order negative inductor.

[0088] Filter inductors L 1 and L 2 , filter capacitor C f and filter damping resistor R f constitute an LLC filter circuit. The filter damping resistor R f is connected in series with the filter capacitor and is regarded as a whole to filter out the harmonics introduced by the switching transistors. One end of filter inductor L 1 is connected to the emitter of the second switching transistor V 2 , and the other end of filter inductor L 1 is respectively connected to one end of filter inductor L 2 and filter capacitor C f . The other end of filter inductor L 2 is connected to one end of the sampling resistor R. The other end of the sampling resistor R is connected to an AD digital-to-analog converter, which is used to convert the current between ports A and B into a digital signal. Another AD digital-to-analog converter converts the analog voltage signal between ports A and B into a digital signal for easy processing by the subsequent MCU controller. The other end of filter capacitor C f is connected to filter damping resistor R f , and filter damping resistor R fThe other end is connected to the third switch tube V 3 The collector, grounded capacitor C g One end of the filter damping R f The other end of the capacitor C is connected to ground g The other end of the sampling resistor R is grounded, port A is the other end of the sampling resistor R, and port B is the filter damping R in the LLC filter circuit. f At the other end, the output voltage of the single-phase inverter contains more harmonics. The LLC filter circuit is used to filter out these harmonic signals and improve the output power quality.

[0089] The self-powered module obtains power directly from the drain-source end of the switch tube element, charges the capacitor in the self-powered module to store energy, and supplies power to the gate drive circuit of the switch element and the MCU controller. The DC-DC conversion circuit takes power from the DC side bus to obtain the DC voltage U required by the single-phase full-controlled bridge. DC .

[0090] The MCU controller applies the excitation voltage u to the ports A and B of the fractional-order negative inductor. g (t) and the port current i L (t) is sampled to generate a control signal wave of the switch tube in the fractional-order negative inductance circuit.

[0091] The sinusoidal pulse width modulation module SPWM uses a triangular carrier to modulate the control signal wave output by the MCU controller to generate a control signal for controlling the switch tube.

[0092] The AC properties of fractional-order negative inductance: it blocks AC and passes DC, so it can still be used for filtering; the phase of the voltage lags behind the current by 90°, similar to an ideal positive capacitor, and the DC properties of the negative inductance are consistent with those of a conventional positive inductance.

[0093] The control method of a high-power filter based on fractional-order positive and negative inductors in parallel is proposed in the present invention. Figure 3 As shown, the method includes:

[0094] Step S1: Determine the filter inductance according to the grid-connected power quality requirements The size of the fractional negative inductance is then calculated. and positive inductance The inductance value;

[0095] The current phase characteristics of fractional-order positive inductance and negative inductance are opposite. When the two are connected in parallel, the current phase is opposite. According to the power quality requirements of the grid, the filter inductance value is determined. The fractional negative inductance is then calculated and positive inductance Inductance value, equivalent filter inductance value when inductors are connected in parallel and fractional negative inductance 、 Positive inductance The relationship is as follows:

[0096]

[0097] Among them, is the inductance value of the fractional-order negative inductance, is the inductance value of the fractional-order positive inductance. When tends to , the equivalent inductance after parallel connection is equivalent to a very large inductance in the full frequency band. Such a very large equivalent inductance can replace the traditional large inductance for filtering. The inductance values of the negative inductance and the positive inductance can be determined according to actual needs. The positive inductance is a physical inductance, and its inductance value is generally determined and not easy to adjust. However, the inductance value of the fractional-order negative inductance is its control parameter and can be adjusted flexibly, so that the inductance value of the parallel combination can be adjusted flexibly to meet actual needs.

[0098] For example, when it is necessary to implement an inductor of 20 mH, a positive inductance of 4 mH and a negative inductance of 5 mH can be used in parallel. The inductance values of the negative inductance and the positive inductance can be determined according to actual needs.

[0099] Step S2: Calculate the order of the fractional-order positive inductance based on the voltage and current in the fractional-order positive inductance, and set the order of the negative inductance equal to the order of the positive inductance to obtain the control parameter of the MCU;

[0100] The essence of many physical phenomena in nature has fractional-order characteristics. The inductor is also a fractional-order device. According to the inductance value of the fractional-order negative inductance and the inductance value of the fractional-order positive inductance, calculate the inductive reactance after the parallel connection of the positive and negative inductors as:

[0101]

[0102] Among them, is the order of the fractional-order positive inductance, is the order of the fractional-order negative inductance, , is the fundamental angular frequency of the excitation voltage at both ends of the parallel structure, is the fundamental frequency;

[0103] The essential idea of this method is to make the output current of the negative inductance close to the current amplitude in the branch where the positive inductance is located and have opposite phases by setting the inductance value and order of the negative inductance. Therefore, the current in the main circuit decreases. On the premise of constant voltage, the overall inductive reactance increases. When tends to When the current magnitudes of the two branches are closer, that is, the cancellation effect of the current in the negative inductance branch on the current in the positive inductance branch is more obvious. It can be found through the above calculation of inductive reactance that when When holds. Therefore, in the method of achieving a larger inductance value by paralleling positive and negative inductances, the order of the negative inductance should be set equal to that of the positive inductance. If the orders of the two are different, the current phases on the two branches will deviate, which may make the increase in the inductance value after parallel connection not obvious.

[0104] The voltage-current relationship formula of the positive inductance is: ; where is the voltage applied to the positive inductance, and is the current in the positive inductance.

[0105] In order to adjust the order of the negative inductance to match that of the positive inductance, the Fourier transform is performed on the voltage-current relationship formula of the positive inductance to obtain the following relationship:

[0106] ;

[0107] Taking the logarithm of both sides of the equation, the following expression is obtained:

[0108] ;

[0109] According to the above formula, the order of the positive inductance is obtained. Use a function signal generator to apply a voltage to the positive inductance and change the voltage frequency multiple times (generally in the lower frequency band, between 50 Hz and 200 Hz, and the experiment can also be flexibly designed according to actual applications for measurement).

[0110] Then adjust the order of the fractional-order negative inductance to be consistent with that of the positive inductance, so as to ensure that the current phases in the two branches differ by 180°. Finally, adjust the equivalent inductance value of the fractional-order negative inductance so that the overall inductance value after parallel connection meets the required inductance value.

[0111] Step S3: Obtain the voltage of the external excitation at both ends of port A and B of the fractional-order negative inductance and the port current , and set the internal parameter auxiliary resistance of the fractional-order negative inductance and the output voltage

[0112] of the DC-DC conversion circuit, and generate a gate drive control signal according to the control strategy; Step S31: Setting of the auxiliary resistance in the fractional-order negative inductance and the output voltage of the DC-DC conversion circuit, in the equivalent inductance value After setting, the amplitude of the triangular carrier wave used by the sine pulse width modulation module SPWM is set to 1, and by adjusting and to simultaneously satisfy the following relationship, the signal wave generated by the MCU controller has an amplitude range of , so that the single-phase inverter used to equivalent the fractional-order negative inductor can work properly:

[0113]

[0114] Among them, , is the amplitude of the external excitation voltage, is the fundamental angular frequency of the external excitation voltage signal, and the voltage proportionality coefficient ;

[0115] Step S32: In each sampling period, the voltage of the external excitation across the two ends of the fractional-order negative inductor port and the port current are sampled by the sensor, and the sampling results are input into the MCU controller:

[0116] Step S33: Generate the signal wave of bipolar modulation in the fractional-order negative inductor topology. The mathematical model of the fractional-order negative inductor is expressed as follows:

[0117]

[0118] Among them, β is the order of the fractional-order negative inductor, is the inductance value of the fractional-order negative inductor, is the excitation voltage across the two ends of the fractional-order negative inductor port in the frequency domain representation, is the frequency domain representation of the port current .

[0119] The phase angle by which the voltage of the fractional-order negative inductor leads the current is: ;

[0120] Therefore, for a 1st-order fractional-order negative inductor, the current leads the voltage by 90° in phase.

[0121] There is the following relationship between the external excitation voltage and the port current of the fractional-order negative inductor and on both sides of the sampling resistor:

[0122]

[0123] Among them, is the filtered voltage signal, R is the sampling resistor, is the fractional-order differential operator.

[0124] After simplification, we get:

[0125]

[0126] Since the phase of the inverter output is the same as that of the modulation signal and the amplitudes are proportional, the signal wave of the MCU controller is obtained as:

[0127]

[0128] Among them, the voltage proportionality coefficient , is the amplitude of the triangular carrier wave, is the output DC voltage of the DC-DC conversion circuit, is the fractional-order integration operator, and are reciprocals of each other.

[0129] The control block diagram of the fractional-order negative inductor ignoring the influence of the filter circuit is as shown in Figure 4 shown.

[0130] For the fractional-order integration operator , the Oustaloup filter is used for approximate calculation. Generally, the frequency band of interest can be selected as (10e-5, 10e+5) Hz. The straight-line characteristic of the fractional-order integration operator is approximated by using broken lines. All these broken lines are generated by integer-order zeros and poles, so that the asymptotic slope of the amplitude-frequency characteristic curve alternates between 0 dB / dec and -20 dB / dec. Such a frequency-domain response characteristic itself will approximate a slant line well, as shown in Figure 5 shown.

[0131] The method of using the Oustaloup filter to approximately calculate the fractional-order integration operator is as follows:

[0132]

[0133] Among them, the zeros and poles of the Oustaloup filter are calculated as follows:

[0134]

[0135] Among them, is the order of the filter, and are the lower and upper frequency limits of the selected frequency band respectively. The fractional-order integration operator of any order can be regarded as the product of the fractional-order integration operator of and the integer-order integration operator.

[0136] For example, if the selected frequency band is (10e-5, 10e+5), the filter order is 5, and the orders are 0.5 and 1.2 respectively, the filter form equivalent to the fractional-order integration operator obtained is as follows:

[0137] The response of the fractional-order integration operator to a sine signal is as follows:

[0138]

[0139] It can be found that it contains two DC components and , which are caused by the integration initial value and the filter response respectively. In order to obtain the AC component therein, a low-pass filter is used to extract the DC component so as to obtain the AC component therein. A sine signal with an amplitude of 150 and a frequency of 2000 Hz is input into the 1.2-order fractional-order integration operator for operation, and the DC offset is further eliminated, as Figure 7 shown.

[0140] The above derivation does not consider the influence of the LLC filter circuit. Considering the filter inductance and in the LLC filter circuit as well as the filter capacitor can make the obtained fractional-order negative inductor model more accurate. During normal operation, the phase deviation caused by the filter circuit is smaller, and the fitting effect on the phase is better.

[0141] The parameters of each component in the fractional-order negative inductor circuit have the following relationship:

[0142]

[0143] Among them, is the voltage of the filter capacitor branch, is the current of the filter capacitor branch, is the current flowing through the filter inductance , is the output voltage of the single-phase inverter, that is, the voltage between the emitter of the second switch tube V2 and the collector of the third switch tube V3.

[0144] Therefore, the signal wave of the MCU controller considering the influence of the LLC filter circuit is:

[0145]

[0146] Among them:

[0147]

[0148] The control block diagram of the fractional-order negative inductor considering the influence of the filter circuit is as follows Figure 6 As shown, the generation methods of these two signal waves can be determined according to the actual application scenarios.

[0149] Step S34: The sine pulse width modulation module SPWM performs sine pulse width modulation on the signal wave and the local triangular carrier wave, thereby generating control signals for the four switching devices.

[0150] The H-bridge equivalent structure and control method of the full-band fractional-order negative inductor of the present invention can exhibit the inductive reactance characteristics of the fractional-order negative inductor in the full band, that is, it is not necessary to modify the control parameters of the fractional-order negative inductor according to the frequency of the excitation at both ends of the port. The fractional-order negative inductor in the present invention is applicable to the full band, so it can be used in application scenarios with a high harmonic content to achieve the filtering function.

[0151] For the control method of the H-bridge equivalent structure of the full-band fractional-order negative inductor of the present invention, assume that there is only a sine-type voltage signal with a specific frequency at both ends of the fractional-order negative inductor port , substitute it into the calculation formula of the signal wave and perform the inverse Laplace transform to obtain:

[0152]

[0153] According to the above formula, it can be found that when the frequency is higher, the second term gradually approaches zero, then there is , that is

[0154] When the frequency is infinite, the voltage signal at both ends of the auxiliary resistor has an increasingly smaller phase difference, the phases tend to be the same, the amplitude difference is increasingly smaller, and the output current of the port tends to zero. Therefore, the fractional-order negative inductor exhibits a high inductive reactance under high-frequency excitation and a low inductive reactance under low-frequency excitation. According to the superposition theorem, the fractional-order negative inductor has a strong ability to block high-frequency signals on a line containing multiple harmonics, so filtering can be achieved.

[0155] Step S4: Check whether the filtering result of the positive and negative inductor parallel filter meets the power quality requirements, and further adjust the positive and negative inductor parameters.

[0156] To verify the feasibility of the high-power filter based on the parallel connection of fractional-order positive and negative inductors, according to Figure 1 , Figure 3 and Figure 5 Build a simulation module in MATLAB, set the predetermined control parameters according to Table 1, start running the simulation, and obtain the following simulation results:

[0157] Table 1 Internal circuit device parameters, control parameters, and applied excitation parameters of the fractional-order negative inductor

[0158]

[0159] According to the second, third, and fourth groups of simulation data in Table 1, the simulation results are respectively as Figure 8 , Figure 9 , Figure 10 shown. The current leads the voltage by 90° in phase, and the current continuously decreases as the frequency increases, indicating that the terminal inductive reactance of the full-band fractional-order negative inductor described in the present invention will increase as the frequency increases.

[0160] According to the first, third, and fifth groups of simulation data in Table 1, the simulation results are respectively as Figure 11 , Figure 9 , Figure 12 shown. Keeping the applied excitation unchanged and changing the order of the fractional-order negative inductor, it can be found that as the order increases, its terminal inductive reactance increases and the port current decreases, indicating that the terminal inductive reactance of the full-band fractional-order negative inductor described in the present invention will increase as the order increases.

[0161] A signal with a fundamental frequency of 50 Hz is added with high-order harmonics and applied across the full-band fractional-order negative inductor. The simulation result is as Figure 13 shown, and the harmonic analysis of the two signals is as Figure 14 and Figure 15 shown. The Total Harmonic Distortion (THD) content of the voltage signal is 17%, and the Total Harmonic Distortion (THD) content of the inductor current is 4.08%. It can be seen that the full-band fractional-order negative inductor has a very obvious inhibitory effect on high-frequency signals and can exhibit the inductive reactance characteristics of a negative inductor in the full band.

[0162] When a positive inductor and a negative inductor are connected in parallel, their overall inductive reactance will increase significantly, as Figure 16 shown. A 0.4H positive inductor and a 0.5H negative inductor are connected in parallel, and the overall inductance value is 2H. At t = 0.06 s, a 0.5H negative inductor is incorporated, and the current decreases from 0.844 A to 0.1821 A. When the inductance values of the positive inductor and the negative inductor are equal, the inductive reactance tends to infinity, as Figure 17 shown. A 0.4H positive inductor and a 0.4H negative inductor are connected in parallel. At t = 0.06 s, a 0.4H negative inductor is incorporated, and the current decreases from 0.844 A to 0.0720 A. It can be seen that when the positive and negative inductors are connected in parallel, their inductive reactance increases significantly.

[0163] Through simulation verification, it can be concluded that the port characteristics of the equivalent fractional-order negative inductor in the present invention during normal operation satisfy the properties of the fractional-order negative inductor, and can respond in the full frequency band. It can be applied to a filtering circuit with complex harmonic content. Through the control method of the high-power filter proposed by the present invention, the structure of the parallel connection of fractional-order positive and negative inductors can exhibit the performance of a large-inductance inductor with a small-inductance inductor, further indicating that the present invention can reduce the volume of the filter, improve the power density, and reduce the cost.

[0164] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-power filter based on fractional-order positive and negative inductors in parallel, characterized in that: The filter includes a fractional-order negative inductor L β and the positive inductance L0, the two are in parallel relationship; Fractional negative inductance L β It includes: a first switch tube V1, a second switch tube V2, a third switch tube V3, a fourth switch tube V4, filter inductors L1 and L2, and a filter capacitor C f , filter damping R f , grounding capacitance C g , sampling resistor R, DC-DC conversion circuit, self-power supply module, MCU controller, digital-to-analog converter AD and sinusoidal pulse width modulation module SPWM, all switch tubes are insulated gate bipolar transistors IGBT; The two output ends of the DC-DC conversion circuit, i.e., the DC chopper circuit, are respectively connected to the collector of the first switch tube V1 and the emitter of the third switch tube V3. The first switch tube V1 and the third switch tube V3 are connected in series, and the second switch tube V2 and the fourth switch tube V4 are connected in series. The collector of the second switch tube V2 is connected to one output end of the DC-DC conversion circuit, and the emitter of the fourth switch tube V4 is connected to the other output end of the DC-DC conversion circuit. The emitter of the first switch tube V1 is connected to the collector of the third switch tube V3, the collector of the first switch tube V1 is connected to the collector of the second switch tube V2, the emitter of the second switch tube V2 is connected to the collector of the fourth switch tube V4, and the emitter of the third switch tube V3 is connected to the emitter of the fourth switch tube V4. The gates of the four switch tubes are connected to the gate drive control signal. Both ends of the four switch tubes are connected in parallel with power diodes. The collector of each switch tube is connected to the negative electrode of the diode, and the emitter of each switch tube is connected to the positive electrode of the diode. Filter inductors L1 and L2, filter capacitors C f and filter damping R f The LLC filter circuit is responsible for filtering out the harmonics introduced by the switch tube. The filter damping R f With filter capacitor C f One end of the filter inductor L1 is connected in series with the emitter of the second switch tube V2, and the other end of the filter inductor L1 is connected to the filter inductor L2 and the filter capacitor C f The other end of the filter inductor L2 is connected to one end of the sampling resistor R, and the other end of the sampling resistor R is connected to an AD digital-to-analog converter, which is used to convert the current i between the A and B ports L (t) is converted into a digital signal. Another AD converter converts the analog voltage signal between the A and B ports into a digital signal. The filter capacitor C f The other end of the filter damping R f Connected, filter damping R f The other end is connected to the collector of the third switch tube V3 and the grounding capacitor C g One end of the filter damping R f The other end of the capacitor C is connected to ground g The other end of the sampling resistor R is grounded, port A is the other end of the sampling resistor R, and port B is the filter damping R in the LLC filter circuit. f the other end.

2. The high power filter according to claim 1, characterized in that: Four switching tubes form a single-phase inverter. In normal operation, the control signal controls the first state that the switching tubes V1 and V4 are turned on at the same time, and the switching tubes V2 and V3 are turned off. The second state is that the switching tubes V1 and V4 are turned off, and the switching tubes V2 and V3 are turned on at the same time.

3. The high power filter according to claim 1, characterized in that: The self-powered module directly obtains power from the drain-source end of the switch tube element, charges the capacitor therein and stores energy. The self-powered module supplies power to the gate drive circuit of the switch element and the MCU controller. The DC-DC conversion circuit takes power from the DC side bus to obtain the DC voltage U required by the single-phase full-controlled bridge. DC ; The MCU controller applies the excitation voltage u to the ports A and B of the fractional-order negative inductor. g (t) and the port current i L (t) performing sampling to generate a control signal wave of a switch tube in a fractional-order negative inductance circuit; The sinusoidal pulse width modulation module SPWM uses a triangular carrier to modulate the control signal wave output by the MCU controller to generate a control signal for controlling the switch tube.

4. A control method for a high-power filter with fractional-order positive and negative inductors in parallel based on any one of claims 1 to 3, characterized in that: The method comprises the following steps: Step S1: Determine the filter inductance value L according to the grid-connected power quality requirements eq Then calculate the fractional negative inductance L β and the inductance value of the positive inductor L0; Step S2: Calculate the order of the fractional-order positive inductor according to the voltage and current in the fractional-order positive inductor, and set the order of the negative inductor to be equal to the order of the positive inductor to obtain the control parameters of the MCU; Step S3: Obtain the external excitation voltage u at both ends of the fractional-order negative inductor ports A and B g (t) and the port current i L (t), and set the fractional order negative inductance L β Internal parameters of auxiliary resistance R and output voltage U of DC-DC conversion circuit DC , generating a gate drive control signal according to a control strategy; Step S4: Check whether the filtering result of the positive and negative inductance parallel filter meets the power quality requirements, and further adjust the positive and negative inductance parameters.

5. The control method according to claim 4, characterized in that: The step S1 further includes: determining the equivalent filter inductance value L when the inductors are connected in parallel eq Then, according to the expression Calculate the inductance L of the fractional negative inductor β And the inductance value L0 of the fractional-order positive inductor.

6. The control method according to claim 4, characterized in that: The step S2 further includes: setting the voltage-current relationship of the positive inductor to: Among them, U L is the voltage applied to the positive inductor, I L is the current in the positive inductor, and according to Calculate the order of positive inductance β + , set the order of the negative inductance to be equal to the order of the positive inductance, and finally adjust the equivalent inductance of the fractional-order negative inductance so that the overall inductance after parallel connection meets the required inductance.

7. The control method according to claim 4, characterized in that: The step S3 further comprises: Step S31: Auxiliary resistor R in fractional-order negative inductor and output voltage U of DC-DC converter circuit DC Satisfies the following relationship: Among them, V is the triangle carrier amplitude used by the sinusoidal pulse width modulation module SPWM, U g is the amplitude of the external excitation voltage, ω is the fundamental angular frequency of the external excitation voltage signal, and the voltage proportionality coefficient Step S32: In each sampling period, the voltage u of the external excitation at both ends of the fractional-order negative inductance port is measured by the sensor. g (t) and the port current i L (t) Perform sampling and input the sampling results into the MCU controller; Step S33: Generate a bipolar modulated signal wave in the fractional-order negative inductor topology structure. Without considering the influence of the LLC filter circuit, the following relationship exists between the external excitation voltage and the port current of the fractional-order negative inductor and the two sides of the sampling resistor: Among them, L β is the inductance of the fractional negative inductor, U g (s) is the excitation voltage u at both ends of the fractional-order negative inductance port g (t) is represented in the frequency domain, I L (s) is the port current i L (t) is represented in the frequency domain, U L (s) is the filtered voltage signal, R is the sampling resistor, s β is a fractional differential operator; The signal wave of the MCU controller is: Among them, the voltage proportionality coefficient V is the amplitude of the triangular carrier, U DC is the output DC voltage of the DC-DC converter circuit, s -β is a fractional integral operator, s β and -β The two are reciprocal; Step S34: the sinusoidal pulse width modulation module SPWM performs sinusoidal pulse width modulation on the signal wave and the local triangular carrier, thereby generating control signals for the four switch devices.

8. The control method according to claim 7, characterized in that: In step S33, the filter inductors L1 and L2 and the filter capacitor C in the LLC filter circuit are considered. f In this case, the signal wave calculation method of the MCU controller is as follows: The parameters of the components in the fractional-order negative inductance circuit have the following relationship: Among them, U c (s) is the voltage of the filter capacitor branch, I c (s) is the current in the filter capacitor branch, I1(s) is the current flowing through the filter inductor L1, and U h (s) is the output voltage of the single-phase inverter, that is, the voltage between the emitter of the second switch tube V2 and the collector of the third switch tube V3; At this time, the signal wave U of the MCU controller ′ M (s) is: U ′ M (s)=K s [G1(s)U g (s)-G2(s)I L (s)]; in:

Images