阅读说明：本技术 一种单相分数阶buck型交流斩波器及其参数设计方法 (Single-phase fractional-order buck type alternating-current chopper and parameter design method thereof ) 是由 王东东 于 2019-10-28 设计创作，主要内容包括：本发明公开了一种单相分数阶buck型交流斩波器及其参数设计方法,包括交流电压源(u<Sub>i</Sub>)、开关管(S<Sub>1</Sub>、S<Sub>2</Sub>、S<Sub>3</Sub>和S<Sub>4</Sub>)、与开关管(S<Sub>1</Sub>、S<Sub>2</Sub>、S<Sub>3</Sub>和S<Sub>4</Sub>)反并联的二极管、输入端分数阶滤波电容(Ci)、输出端分数阶滤波电容(C<Sub>f</Sub>)、输出端分数阶滤波电感(L)和负载(R<Sub>L</Sub>)；本发明采用分数阶元件实现的单相分数阶buck型交流斩波器,完全区别于以往的AC/AC变换电路,它增加了滤波电路参数的控制维度,通过参数设计选取输出分数阶滤波电容C<Sub>f</Sub>的阶数、分数阶滤波电感元件的阶数和分数阶滤波电容C<Sub>i</Sub>的阶数,大大降低了电压谐波畸变率和电流谐波畸变率,可以提高低占空比时的输入功率因数。(The invention discloses a single-phase fractional buck type alternating-current chopper and a parameter design method thereof i ) And a switching tube (S) 1 、S 2 、S 3 And S 4 ) And a switching tube (S) 1 、S 2 、S 3 And S 4 ) Anti-parallel diode, input end fractional order filter capacitor (Ci) and output end fractional order filter capacitor (C) f ) An output terminal fractional order filter inductor (L) and a load (R) L ) (ii) a The single-phase fractional-order buck type alternating-current chopper realized by adopting the fractional-order element is completely different from the conventional AC/AC conversion circuit, the control dimension of the parameter of the filter circuit is increased, and the selection is performed through parameter designOutput fractional order filter capacitor C f Order of the filter inductance element, order of the fractional filter inductance element and the fractional filter capacitance C i The order of the voltage harmonic distortion factor and the current harmonic distortion factor is greatly reduced, and the input power factor under the condition of low duty ratio can be improved.)

1. A single-phase fractional buck type alternating current chopper is characterized in that: comprising an alternating voltage source (u)_i) And a switching tube (S)₁、S₂、S₃And S₄) And a switching tube (S)₁、S₂、S₃And S₄) Anti-parallel diode, input end fractional order filter capacitor (Ci) and output end fractional order filter capacitor (C)_f) An output terminal fractional order filter inductor (L) and a load (R)_L) (ii) a AC voltage source (u)_i) The two ends of the input end fractional order filter capacitor (Ci) are connected into the switch tube (S) respectively₁) And a switch tube (S)₂) Switch tube (S)₃) And a switch tube (S)₄) After being connected in series with a switch tube (S)₁) And a switch tube (S)₂) Is connected to the output terminal of the filter capacitor (C)_f) Is connected with an output end fractional order filter inductor (L) in series, and one end of the output end fractional order filter inductor (L) is connected with a switch tube (S)₁) Output terminal of (1), output terminal fractional order filter capacitor (C)_f) One end of (S) is connected to the switch tube₂) Through the switch tube (S)₁And S₂) And its anti-parallel diode will exchange the voltage source (u)_i) Via an output-side fractional order filter capacitor (C)_f) And an output terminal fractional order filter inductor (L) to the load (R)_L) Outputting sine wave voltage or feeding back electric energy to the alternating current power supply by a load; the working principle of the circuit breaker lies in four switching tubes (S)₁、S₂、S₃And S₄) And three working modes are formed by alternate conduction.

2. The single-phase fractional-order buck-type ac chopper of claim 1, wherein: the input terminal fractional order filter capacitance (Ci) and the output terminal fractional order filter capacitance (C)_f) The time domain relation of the voltage and the current satisfies the equation:the phase relation satisfies:whereinIn the form of a fractional order differential operator,as a fractional order integral operator, i_C(t) is the current through the fractional filter capacitor, u_CAnd (t) is the voltage at two ends of the fractional order filter capacitor, alpha is the order, and C is the capacitance value. The fractional order filter capacitance has a phasor form:here, X_C＝1/((jω)^αC) Defined as a fractional order capacitive reactance.

3. The single-phase fractional-order buck-type ac chopper of claim 1, wherein: the voltage and the current of the output end fractional order filter inductor (L)The time domain relationship satisfies the equation: the phase relation satisfies:wherein u is_LIs the voltage across a fractional order filter inductor, i_LIs the current through the fractional filter inductor, beta is the order and L is the inductance value. The fractional order filter inductance has a phasor form:wherein, X_L＝ω^αL is defined as a fractional order inductive reactance.

4. The single-phase fractional-order buck-type ac chopper of claim 1, wherein: the three working modes are respectively a power transmission working mode, a dead zone working mode and a follow current working mode; when in the power transmission working mode, the switch tube (S)₁) And a switching tube (S)₂) And a switching tube (S)₄) Conducting, switching tube (S)₃) When the power is cut off, the energy is transmitted from the power supply to the load or fed back from the load to the power supply, and when the power is in the dead-zone working mode, the switch tube (S) is switched on or off₂) And a switching tube (S)₄) Conducting, switching tube (S)₁) And a switching tube (S)₃) When the inductor current is cut off, the inductor current passes through the switch tube (S)₃) And a switching tube (S)₄) Follow current or through a switch tube (S)₁) And a switching tube (S)₂) Feedback energy, switching the tube (S) when in the follow current mode of operation₂) And a switching tube (S)₃) And a switching tube (S)₄) Conducting, switching tube (S)₁) Cut-off, fractional order filtering of the inductor current through the switching tube (S)₃) And a switching tube (S)₄) And then follow current.

5. A single phase fraction as claimed in claims 1 to 4The parameter design method of the order buck type alternating-current chopper is characterized by comprising the following steps: the method comprises the following steps: (1) calculating voltage harmonic distortion rate THD of fractional order filter capacitor at output end_uAnd an output terminal fractional order filter capacitor (C)_f) The order of the output-side fractional order filter inductance (L); calculating the harmonic distortion rate THD of the fractional order filter inductor (L) current at the output_iA relation to the order of the fractional order filter inductance (L) at the output; (2) calculating input power factorAnd input end fractional order filter capacitor C_iThe order of (a).

Technical Field

The invention relates to the technical field of AC/AC conversion, in particular to a single-phase fractional-order buck type alternating-current chopper and a parameter design method thereof.

Background

The alternating current conversion circuit is widely applied to the national defense field of aviation, aerospace and the like and the civil field of power systems, new energy power generation and the like, and the energy conversion is more efficient due to the fact that an intermediate direct current link is omitted, so that the alternating current conversion circuit is increasingly important at the present day that fossil energy is increasingly nervous, particularly in the field of wind power generation, the alternating current conversion circuit can realize the function of directly merging alternating current energy into a power grid or supplying alternating current load, and therefore research on the conversion and control technology of the alternating current conversion circuit plays an important role in development and utilization of new energy.

The traditional pulse width modulation AC-AC chopper circuit has the advantages of simple circuit topology, high electric energy transmission efficiency, high network side power factor and the like, and is widely applied, however, because the filter circuit adopts the traditional passive inductance-capacitance filter circuit, on one hand, the filter effect is limited, on the other hand, because the inductance-capacitance is actually a fractional order element, the filter effect of the filter circuit obtained by adopting an integer order parameter design method can generate errors with an actual circuit, and the errors caused by the fractional order property are particularly obvious in low frequency or high frequency.

The fractional calculus theory can be applied and developed rapidly in various subject fields, particularly in the fields of automatic control, nano materials and the like, besides the fact that the fractional calculus theory can accurately simulate physical phenomena in nature, the fractional calculus theory can also be used as an additional control dimension to increase the controllability of a main circuit or a control circuit, and the method brings infinite vitality for the development of the field of industrial control.

In view of the advantages of the parameter optimization design by using the fractional calculus theory, it is necessary to provide a single-phase fractional buck type ac chopper.

Disclosure of Invention

In view of the above-mentioned deficiencies of the prior art, the present invention provides a single-phase fractional buck-type ac chopper and a method for designing parameters thereof.

The purpose of the invention is realized as follows:

a single-phase fractional-order buck-type AC chopper comprises an AC voltage source (u)_i) And a switching tube (S)₁、S₂、S₃And S₄) And a switching tube (S)₁、S₂、S₃And S₄) Anti-parallel diode and input endFractional order filter capacitor (Ci) and output end fractional order filter capacitor (C)_f) An output terminal fractional order filter inductor (L) and a load (R)_L) (ii) a AC voltage source (u)_i) The two ends of the input end fractional order filter capacitor (Ci) are connected into the switch tube (S) respectively₁) And a switch tube (S)₂) Switch tube (S)₃) And a switch tube (S)₄) After being connected in series with a switch tube (S)₁) And a switch tube (S)₂) Is connected to the output terminal of the filter capacitor (C)_f) Is connected with an output end fractional order filter inductor (L) in series, and one end of the output end fractional order filter inductor (L) is connected with a switch tube (S)₁) Output terminal of (1), output terminal fractional order filter capacitor (C)_f) One end of (S) is connected to the switch tube₂) Through the switch tube (S)₁And S₂) And its anti-parallel diode will exchange the voltage source (u)_i) Via an input-output fractional order filter capacitor (C)_f) And an output terminal fractional order filter inductor (L) to the load (R)_L) Outputting sine wave voltage or feeding back electric energy to the alternating current power supply by a load; the working principle of the circuit breaker lies in four switching tubes (S)₁、S₂、S₃And S₄) And three working modes are formed by alternate conduction.

The input terminal fractional order filter capacitance (Ci) and the output terminal fractional order filter capacitance (C)_f) The time domain relation of the voltage and the current satisfies the equation:the phase relation satisfies:whereinIn the form of a fractional order differential operator,as a fractional order integral operator, i_C(t) is the current through the fractional filter capacitor, u_C(t) is two ends of a fractional order filter capacitorα is the order, and C is the capacitance. The fractional order filter capacitance has a phasor form:here, X_C＝1/((jω)^αC) Defined as a fractional order capacitive reactance.

The time domain relation of the voltage and the current of the output end fractional order filter inductor (L) meets the equation:the phase relation satisfies:wherein u is_LIs the voltage across a fractional order filter inductor, i_LIs the current through the fractional filter inductor, beta is the order and L is the inductance value. The fractional order filter inductance has a phasor form:wherein, X_L＝ω^αL is defined as a fractional order inductive reactance.

The three working modes are respectively a power transmission working mode, a dead zone working mode and a follow current working mode; when in the power transmission working mode, the switch tube (S)₁) And a switching tube (S)₂) And a switching tube (S)₄) Conducting, switching tube (S)₃) When the power is cut off, the energy is transmitted from the power supply to the load or fed back from the load to the power supply, and when the power is in the dead-zone working mode, the switch tube (S) is switched on or off₂) And a switching tube (S)₄) Conducting, switching tube (S)₁) And a switching tube (S)₃) When the inductor current is cut off, the inductor current passes through the switch tube (S)₃) And a switching tube (S)₄) Follow current or through a switch tube (S)₁) And a switching tube (S)₂) Feedback energy, switching the tube (S) when in the follow current mode of operation₂) And a switching tube (S)₃) And a switching tube (S)₄) Conducting, switching tube (S)₁) Cut-off, fractional order filtering of the inductor current through the switching tube (S)₃) And a switching tube (S)₄) And then follow current.

Single-phase fractional order buck type alternating current choppingA method of designing parameters for a wave filter, comprising the steps of: (1) calculating voltage harmonic distortion rate THD of fractional order filter capacitor at output end_uAnd an output terminal fractional order filter capacitor (C)_f) The order of the output terminal fractional order filter inductance (L); calculating the harmonic distortion rate THD of the fractional order filter inductor (L) current at the output_iAnd an output terminal fractional order filter capacitor (C)_f) The order of the output terminal fractional order filter inductance (L); (2) calculating input power factorAnd input end fractional order filter capacitor C_iThe order of (a).

The invention has the beneficial effects that: the single-phase fractional buck type alternating-current chopper realized by adopting the fractional order element is completely different from the traditional AC/AC conversion circuit, the control dimensionality of the parameters of the filter circuit is increased, and the output fractional order filter capacitor C is selected through parameter design_fOrder of the filter inductance element, order of the fractional filter inductance element and the fractional filter capacitance C_iThe order of the voltage harmonic distortion factor and the current harmonic distortion factor is greatly reduced, and the input power factor under the condition of low duty ratio can be improved.

Drawings

FIG. 1 is a circuit diagram of the present invention;

FIG. 2 is a current flow diagram for power transfer mode;

FIG. 3 is a current flow diagram for dead band mode;

FIG. 4 is a current flow diagram for freewheel mode;

FIG. 5 is a graph of the fundamental component of the output fractional order filter;

FIG. 6 is a graph of the harmonic component of the output fractional order filter;

FIG. 7 is an input fractional order filter fundamental component;

FIG. 8 illustrates the voltage harmonic distortion of the output fractional order filter capacitor;

FIG. 9 illustrates fractional order filter inductor current harmonic distortion;

fig. 10 is an input power factor.

Detailed Description

The invention is further illustrated by the following figures and examples.

A single-phase fractional-order buck-type AC chopper comprises an AC voltage source (u)_i) And a switching tube (S)₁、S₂、S₃And S₄) And a switching tube (S)₁、S₂、S₃And S₄) Anti-parallel diode, input end fractional order filter capacitor (Ci) and output end fractional order filter capacitor (C)_f) Fractional order filter inductance (L) and load (R) at output end and output end_L) (ii) a AC voltage source (u)_i) The two ends of the input end fractional order filter capacitor (Ci) are connected into the switch tube (S) respectively₁) And a switch tube (S)₂) Switch tube (S)₃) And a switch tube (S)₄) After being connected in series with a switch tube (S)₁) And a switch tube (S)₂) Is connected to the output terminal of the filter capacitor (C)_f) Is connected with an output end fractional order filter inductor (L) in series, and one end of the output end fractional order filter inductor (L) is connected with a switch tube (S)₁) Output terminal of (1), output terminal fractional order filter capacitor (C)_f) One end of (S) is connected to the switch tube₂) Through the switch tube (S)₁And S₂) And its anti-parallel diode will exchange the voltage source (u)_i) Via an input-output fractional order filter capacitor (C)_f) And an output terminal fractional order filter inductor (L) to the load (R)_L) Outputting sine wave voltage or feeding back electric energy to the alternating current power supply by a load; the working principle of the circuit breaker lies in four switching tubes (S)₁、S₂、S₃And S₄) Conducting in turn to form three working modes, wherein the three working modes are a power transmission working mode, a dead zone working mode and a follow current working mode respectively; when in the power transmission working mode, the switch tube (S)₁) And a switching tube (S)₂) And a switching tube (S)₄) Conducting, switching tube (S)₃) When the power is cut off, the energy is transmitted from the power supply to the load or fed back from the load to the power supply, and when the power is in the dead-zone working mode, the switch tube (S) is switched on or off₂) And a switching tube (S)₄) Conducting, switching tube (S)₁) And a switching tube (S)₃) When the inductor current is cut off, the inductor current passes through the switch tube (S)₃) And a switching tube (S)₄) Follow current or through a switch tube (S)₁) And a switching tube (S)₂) Feedback energy, switching the tube (S) when in the follow current mode of operation₂) And a switching tube (S)₃) And a switching tube (S)₄) Conducting, switching tube (S)₁) Cut-off, fractional order filtering of the inductor current through the switching tube (S)₃) And a switching tube (S)₄) And then follow current.

The input terminal fractional order filter capacitance (Ci) and the output terminal fractional order filter capacitance (C)_f) The time domain relation of the voltage and the current satisfies the equation:the phase relation satisfies:whereinIn the form of a fractional order differential operator,as a fractional order integral operator, i_C(t) is the current through the fractional filter capacitor, u_CAnd (t) is the voltage at two ends of the fractional order filter capacitor, alpha is the order, and C is the capacitance value. The fractional order filter capacitance has a phasor form:here, X_C＝1/((jω)^αC) Defined as a fractional order capacitive reactance. The time domain relation of the voltage and the current of the output end fractional order filter inductor (L) meets the equation:the phase relation satisfies:wherein u is_LIs the voltage across a fractional order filter inductor, i_LIs the current through the fractional filter inductor, beta is the order and L is the inductance value. The fractional order filter inductance has a phasor form:wherein, X_L＝ω^αL is defined as a fractional order inductive reactance.

A parameter design method for a single-phase fractional buck type alternating-current chopper comprises the following steps: (1) calculating voltage harmonic distortion rate THD of fractional order filter capacitor at output end_uAnd an output terminal fractional order filter capacitor (C)_f) The order of the output terminal fractional order filter inductance (L); calculating the harmonic distortion rate THD of the fractional order filter inductor (L) current at the output_iAnd an output terminal fractional order filter capacitor (C)_f) The order of the output terminal fractional order filter inductance (L); (2) calculating input power factorAnd a fractional order filter capacitor C_iThe order of (a).

The method comprises the following specific steps: as shown in fig. 1, which is a schematic diagram of a single-phase fractional-order buck-type ac chopper of the present invention, in fig. 1, three operation modes, i.e., power transmission, dead zone, and freewheeling, exist within one high-frequency switching period; when in power transmission mode, the switch tube S₁Switch tube S₂Switch tube S₄Conducting, switching tube S₃Cut off, energy is transmitted from the power supply to the load or fed back to the power supply by the load; when in the dead zone mode, the switching tube S₂Switch tube S₄Conducting, switching tube S₁Switch tube S₃When the inductive current is cut off, the inductive current passes through the switch tube S₃Switch tube S₄Follow current or through switch tube S₁Switch tube S₂Feeding back energy; when in the freewheeling mode, the switch tube S₂Switch tube S₃Switch tube S₄Conducting, switching tube S₁Cut-off, fractional order filtering inductor current through switch tube S₃Switch tube S₄And then follow current. In the circuit of the single-phase fractional-order buck-type AC chopperThe input and output filter elements are fractional order elements. As shown in fig. 1, the single-phase fractional buck ac chopper has fractional filtering elements at both the input and output ends, and thus needs to be designed.

Firstly, let the input AC power supply be

Where ω is the angular frequency, U_iIs an effective value.

Then, the Fourier series of the switching function is

Wherein D is the duty cycle, ω_sIs the switching angular frequency.

The front-end voltage u of the output filter can thus be obtained_f(t) is

The equivalent circuit of the fundamental wave and the harmonic component of the filter at the input end and the output end of the single-phase fractional buck type alternating-current chopper is shown in the figures 5-7. The output end fractional order filter capacitor voltage fundamental component can be obtained from the graph 5Is composed of

Wherein the content of the first and second substances,thus is provided with

From FIG. 6Obtaining the voltage harmonic component of the output terminal fractional order filter capacitorIs composed of

Wherein the content of the first and second substances,ω′＝kω_sand + -omega. Thus is provided with

Due to the switching angular frequency omega_sMuch higher than the angular frequency of the power supply, and thus has

kω_s±ω≈kω_s

The harmonic distortion of the fractional order filter capacitor voltage at the output end can be calculated by the formulas (2) and (4)

From the foregoing analysis, THD_uNot only the output end fractional order filter inductance value L and the output end fractional order filter capacitance value C_fAnd also to their corresponding order.

Similarly, the fundamental component of the inductor current is obtained by fractional filtering

Thus is provided with

The k-th harmonic component of the fractional filter inductor current is

Thus is provided with

The total harmonic distortion of the fractional filter inductor L current is

From the foregoing analysis, THD_iNot only the output end fractional order filter inductance value L and the output end fractional order filter capacitance value C_fAnd also to their corresponding order.

When the circuit parameter values are: switching frequency f_s＝20kHz，C_f＝10uF，R_LWhen L is 0.6mH and k is 6, the fractional order filter capacitor C is arranged at the output end_fHarmonic distortion rate THD of voltage_uAs shown in FIG. 8, it can be seen that when the order of the output terminal fractional order filter inductor L is 1, the output terminal fractional order filter capacitor C follows the output terminal fractional order filter inductor L_fIs increased, and the fractional order of the output end of the filter capacitor C is increased_fHarmonic distortion rate THD of voltage_uThe smaller; fractional order filter capacitor C at output end_fWhen the order of the output end fractional order filter inductor L is 1, the output end fractional order filter capacitor C rises along with the rise of the order of the output end fractional order filter inductor L_fHarmonic distortion rate THD of voltage_uThe smaller; when the circuit parameter values are: switching frequency f_s＝20kHz，C_f＝10uF，R_LWhen L is 0.6mH, k is 6, the harmonic distortion THD of the L current of the output fractional order filter inductor is 16.1 Ω_iThe relationship with the circuit parameters, as shown in FIG. 9, can be seen when the fractional order filter capacitor C is at the output_fWhen the order of the output end fractional order filter inductor L is 1, the harmonic distortion rate THD of the current of the output end fractional order filter inductor L increases along with the increase of the order of the output end fractional order filter inductor L_iThe smaller. Thus, the desired output can be obtained by selecting the appropriate fractional order of the elementsFractional order filter capacitor C_fHarmonic distortion rate THD of voltage_uAnd harmonic distortion rate THD of output end fractional order filter inductor L current_i。

The input power factor of the circuit can be obtained by an equivalent circuit shown in fig. 7. Input current of

When the circuit parameter values are: the input and output voltage frequency is 50Hz, C_f＝10uF，R_L＝16.1Ω，L＝0.6mH，C_iWhen 1.2uF, 1 β, the input power factorAs shown in fig. 10, it is understood that the power factor at a low duty ratio can be improved when the order of the input-side fractional filter capacitance (Ci) is lowered.