WO2018023919A1 - 一种阶数大于1的大功率可调高频分数阶电容及其控制方法 - Google Patents

一种阶数大于1的大功率可调高频分数阶电容及其控制方法 Download PDF

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WO2018023919A1
WO2018023919A1 PCT/CN2016/110552 CN2016110552W WO2018023919A1 WO 2018023919 A1 WO2018023919 A1 WO 2018023919A1 CN 2016110552 W CN2016110552 W CN 2016110552W WO 2018023919 A1 WO2018023919 A1 WO 2018023919A1
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fractional
input
current
voltage
frequency
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French (fr)
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张波
江彦伟
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华南理工大学
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K7/00—Modulating pulses with a continuously-variable modulating signal
    • H03K7/08—Duration or width modulation ; Duty cycle modulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/538—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a push-pull configuration
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03K—PULSE TECHNIQUE
    • H03K5/00—Manipulating of pulses not covered by one of the other main groups of this subclass
    • H03K5/13—Arrangements having a single output and transforming input signals into pulses delivered at desired time intervals
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0003—Details of control, feedback or regulation circuits
    • H02M1/0012—Control circuits using digital or numerical techniques
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/4815—Resonant converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

Definitions

  • the invention relates to the technical field of fractional order device construction, and particularly relates to a high power adjustable high frequency fractional capacitor with an order greater than one and a control method thereof.
  • Fractional calculus has a history of more than 300 years, which extends the order of calculus from integer to fraction or even complex. Fractional calculus can reveal some phenomena in nature more realistically. In fact, integer-order capacitors are not inherent in nature. They are components with fractional properties. However, most of the capacitors currently used in practice are connected to the order of 1, which can be completely ignored for the fractional order. However, if the fractional nature of the capacitor can be utilized and the fractional capacitance of different orders, capacitances and powers is purposefully designed, then a new application area of the capacitor can be opened.
  • the present invention provides an adjustable power with an order greater than one.
  • the high-frequency fractional capacitor and the control method thereof specifically, the control signal generated by the controller is used to control the fundamental voltage of the output of the high-frequency controlled voltage source, so that the input current and the input voltage satisfy the definition of the fractional-capacitance, by setting the controller, Fractional capacitances with different values and orders can be implemented.
  • the high-frequency AC controlled voltage source is composed of a high-frequency AC inverter circuit capable of outputting a high-frequency AC voltage, and has the characteristics of flexible working characteristics, adjustable capacitance and order, and the fractional-capacitance power is inversed by high-frequency AC.
  • the variable circuit is determined, so the present invention can realize fractional capacitance of different power levels.
  • a high power adjustable high frequency fractional capacitor having an order greater than one including an AC input module, a coupling impedance, a high frequency AC controlled voltage source, an AC input sampling module, a controller, an end of the AC input module and a coupling impedance One end is connected, the other end of the coupling impedance is connected to the positive output end of the high frequency AC controlled voltage source, the negative output end of the high frequency AC controlled voltage source is connected to the other end of the AC input module, and the AC input sampling module samples the input current I In and the input voltage V in get the amplitude I inm and phase of the input current I in And the magnitude V inm and phase of the input voltage V in And sent to the controller, the controller processes the sampled signal according to the fractional-capacitance current closed-loop control algorithm and generates a control signal D to be sent to the high-frequency AC controlled voltage source, and the high-frequency AC controlled voltage source is according to the control signal D A fundamental voltage V F is generated between the positive output terminal and the negative output terminal.
  • controlling the controlled voltage source to output the fundamental voltage V F can make the input current I in an arbitrary waveform in the case where the input voltage V in is known. Therefore, correct control of the output fundamental voltage V F allows the relationship between the input current I in and the input voltage V in to satisfy the definition of the fractional capacitance at the desired frequency.
  • the high-frequency controlled voltage source of the present invention is composed of a high-frequency AC inverter circuit capable of outputting a high-frequency AC voltage, and can output active power to the outside to satisfy the characteristics of the fractional-order capacitor when the order is greater than 1.
  • the basic working principle of the high-frequency AC inverter circuit is to convert the control signal D into a pulse width modulation signal for driving the switch tube in the circuit, thereby controlling the output fundamental voltage V F of the circuit to control the input current I in
  • the relationship between the required frequency and the input voltage V in is in accordance with the relationship of the fractional capacitance current and voltage.
  • the high-frequency AC controlled voltage source is composed of a high-frequency AC inverter circuit capable of outputting a high-frequency AC voltage, and the high-frequency AC controlled voltage source outputs active power to the outside, and the order is greater than 1, by adopting different A controlled voltage source of power capacity that achieves fractional capacitance at different power levels.
  • controller is constructed by a digital signal processor.
  • fractional-capacitance current closed-loop control algorithm is a current closed-loop control algorithm based on phasor analysis, which can avoid voltage-current waveform detection point by point in a high-frequency AC cycle, reduce the burden on the controller, and is easy to implement digitally. .
  • fractional-capacitance current closed-loop control algorithm is implemented on a digital signal processor, and the capacitance and order of the fractional capacitance can be adjusted online by modifying the software parameters online.
  • the fractional-capacitance current closed-loop control algorithm is based on the “phasor analysis” control method, which avoids detecting the voltage and current waveforms point by point in a high-frequency alternating current period, can reduce the burden of the controller, and is easy to implement digitally.
  • the control method of the high-power adjustable high-frequency fractional capacitor with the order greater than 1 specifically includes:
  • V F , V in and I in are both sinusoidal, their waveforms can be described only by frequency, amplitude and initial phase, and can be represented by "phasor analysis". Taking the direction of V in as the real axis and the 90 degree as the imaginary axis, constructing the complex plane, the V F , V in and I in phasor forms and their representations on the complex plane are:
  • V Fm is the amplitude of the controlled source output voltage, respectively.
  • V F_REAL and V F_IMA are respectively The real and imaginary parts, I in_REAL and I in_IMA are The real and imaginary parts.
  • I ref_REAL and I ref_IMA are the real part and the imaginary part respectively
  • C ⁇ is the capacitance of the fractional capacitance
  • ⁇ is the fractional capacitance.
  • the order of the equation is known from the above equation.
  • the relationship between the current given signal I ref and the input voltage V in is the relationship of the fractional capacitance current and voltage.
  • the present invention provides a high-power adjustable high-frequency fractional capacitor with an order greater than one, which can work at an input voltage, that is, a fractional capacitor voltage is high.
  • the relationship between the input current input voltage obtained is exactly the same as the definition of the fractional capacitance with order greater than 1 at the required operating frequency, and the parameters of the controller can be adjusted according to the needs of the application.
  • the order and capacitance of different fractional capacitances are flexibly adjusted, and the fractional capacitance power achieved by the present invention is determined by the controlled voltage source. Therefore, controlled voltage sources of different power levels can be selected to adapt to different power applications.
  • FIG. 1 is a fractional order capacitance model with an order greater than one provided in the embodiment.
  • FIG. 2 is a circuit diagram of a class D resonant inverter in the embodiment.
  • FIG. 3 is a schematic diagram of fractional capacitance simulation in the embodiment.
  • FIG. 4 is a simulation waveform diagram of input voltage and input current of a 1.3th order fractional capacitor in the embodiment.
  • FIG. 5 is a simulation waveform diagram of input voltage and input current of a 1.5-step fractional capacitor in the embodiment.
  • FIG. 6 is a simulation waveform diagram of an input voltage and an input current of a 1.7-order fractional capacitor in the embodiment.
  • Figure 7 is an input current and input voltage waveform of a simulation model in an embodiment.
  • the basic principle of a high-power adjustable high-frequency fractional capacitor with an order greater than 1 in this example is to control the output voltage of the high-frequency AC controlled voltage source with the control signal generated by the controller to make the input current and input of the circuit.
  • a high-power adjustable fractional capacitor with an order greater than 1 includes an AC input module 1, a coupling impedance 2, a high-frequency AC controlled voltage source 3, an AC input sampling module 4, a controller 5, and an AC input.
  • One end A of the module 1 is connected to one end of the coupling impedance 2, and the other end of the coupling impedance 2 is connected to the positive output terminal P of the high frequency AC controlled voltage source 3, and the negative output terminal N of the high frequency AC controlled voltage source 3 and the alternating current
  • the other end B of the input module 1 is connected, and the AC input sampling module 4 samples the input current I in and the input voltage V in to obtain the amplitude I inm and phase of the input current I in .
  • the digital signal processor TMS320F28335 processes the sampled signal according to the fractional capacitance current closed-loop control algorithm and generates the control signal D to the high frequency AC controlled voltage source 3, high frequency communication
  • the controlled voltage source 3 generates a fundamental voltage V F between the positive output terminal P and the negative output terminal N in accordance with the control signal D.
  • the high-frequency controlled voltage source uses a high-frequency AC inverter circuit that can output a high-frequency AC voltage.
  • the high-frequency AC inverter circuit uses a Class D resonant inverter, as shown in Figure 2.
  • C r, L r is a series resonant branch, branch Rl series resonant resistance, two complementary switch is turned on, the duty ratio of the driving waveform is provided on the tube S1 is D, and V in a phase difference
  • the waveform of the voltage V DS across the S2 is a square wave having the same phase as the S1 driving waveform and the amplitude being the DC side voltage value V d .
  • the Fourier decomposition of V DS gives the instantaneous value expression as:
  • w is the switching angular frequency of the high frequency AC inverter circuit is the operating frequency of the fractional capacitance, where n represents the current component as the nth harmonic.
  • Amplitude and duty cycle D ⁇ [0,0.5] in the duty cycle of the fundamental wave interval V F is one to one relationship, and the phase of the fundamental wave V F Phase with the drive waveform The same, so controlling the duty cycle and phase of the drive waveform of S1, the amplitude and phase of V F can be controlled.
  • the digital signal processor converts the sampled voltage and current signals into a phasor expression, with the input voltage V in the real axis, and the 90 degrees as the imaginary axis, and constructing the complex plane, the V F , V in and The I in phasor form and its representation on the complex plane are:
  • I in_REAL and I in_IMA respectively input the current vector The real part and the imaginary part.
  • the digital signal processor performs the following operation on the input voltage phasor to obtain a current given signal. for:
  • C ⁇ and ⁇ are the capacitance and order of the fractional capacitance, respectively, and I ref_REAL and I ref_IMA respectively give the current given signal The real part and the imaginary part.
  • the current closed-loop control algorithm used in the embodiment is proportional control with input voltage feedforward compensation, that is,
  • V F_REAL and V F_IMA are the vectors, respectively The real part and the imaginary part.
  • Figure 3 is a schematic diagram of a high-power fractional-order capacitor with an order greater than 1 in a PSIM environment.
  • the inductor L includes the inductance L r of the series resonant branch and the coupled inductor L f .
  • the fractional-order capacitive current closed-loop control algorithm Executed in the digital signal processor, including equations (3)-(12). The capacitance and order of the fractional capacitance can be adjusted online by modifying the C ⁇ and ⁇ of equation (7) online in the digital signal processor.
  • the input AC voltage be 100V/30kHz
  • the DC power supply voltage be 300V
  • the inductance L 1085uH
  • the capacitance C 26.08nF
  • the internal resistance r 0.8 ⁇ .
  • the input current and the input voltage waveform of the simulation model are as shown in Fig. 7, when the capacitance is 5.5 ⁇ 10 -11 and the order is 1.7.
  • the capacitance and order of the fractional capacitance are 7 ⁇ 10 -9 and 1.3 respectively, and the input current and the input voltage are in phase difference.
  • the above simulation verifies the feasibility and correctness of the present invention.
  • it can output active power to meet the characteristics of fractional capacitance when the order is greater than 1.
  • it can output high frequency AC voltage to meet the requirements of high frequency operation of fractional capacitance.
  • Third, it can be designed and controlled according to the application. Signal, control the output voltage of the high frequency AC inverter circuit, adjust online and realize fractional order of different capacitance and order Capacitor;
  • the power of the fractional capacitor is determined by the rated power of the high-frequency AC inverter circuit.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
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Abstract

一种阶数大于1的大功率可调高频分数阶电容及其控制方法，分数阶电容包括交流输入模块(1)、耦合阻抗(2)、高频交流受控电压源(3)、交流输入采样模块(4)、控制器(5)。控制器(5)根据交流输入采样模块(4)采集到的输入电压信号和输入电流信号，产生相应的控制信号，控制受控电压源(3)的输出电压，使输入电流和输入电压之间符合分数阶电容的电流电压关系。可调高频分数阶电容，可工作在输入电压即分数阶电容电压为高频的时候，所得到的输入电流输入电压之间的关系在所需工作频率处与阶数大于1的分数阶电容的定义完全一致，还可以通过调整控制器的参数，灵活调节实现不同分数阶电容的阶数和容值，还可选用不同功率等级的受控电压源以适应不同的功率应用场合。

Description

一种阶数大于1的大功率可调高频分数阶电容及其控制方法 技术领域
涉及分数阶器件构造技术领域，具体涉及一种阶数大于1的大功率可调高频分数阶电容及其控制方法。
背景技术
分数阶微积分已经有300多年的历史，其将微积分的阶次从整数阶推广到分数甚至复数。分数阶微积分可以更真实的揭示自然界中的一些现象。事实上，整数阶电容器在本质上是不存在的，它是具有分数阶性质的元件，只是目前实际中用的电容器，大部分都是阶数接于1，对于分数阶的情况可以完全忽略。但是，如果可以利用电容器的分数阶性质，有目的的设计不同阶数、容值和功率的分数阶电容，那么就可以开辟电容器的新的应用领域。1964年，美国学者G.E Carlson在论文中根据分数阶微积分的定义首次使用了“分数阶电容”这个概念，并利用牛顿叠代法给出了特定阶次的分数阶电容的无源电路等效模型；此后国内外众多学者利用传统的电阻、电容、电感和运算放大器等提出了多种构造分数阶电容的方案，但都只能适用于毫瓦级的功率，严重地限制了分数阶电容在各种功率场合的应用。也有学者基于分形几何的概念并通过硅工艺制造分数阶电容，但只能在电容阶数小于1的特定范围内实现。
发明内容
针对目前现有技术的缺点与不足，本发明提供阶数大于1的大功率可调 高频分数阶电容及其控制方法，具体是用控制器产生的控制信号控制高频受控电压源输出的基波电压，使输入电流与输入电压满足分数阶电容的定义，通过设置控制器，可实现不同容值和阶数的分数阶电容。高频交流受控电压源是由可输出高频率交流电压的高频交流逆变电路构成，具有工作特性灵活，容值、阶数在线可调的特点，且分数阶电容功率由高频交流逆变电路决定，故本发明可以实现不同功率等级的分数阶电容。
本发明的目的通过如下技术方案实现。
一种阶数大于1的大功率可调高频分数阶电容，包括交流输入模块、耦合阻抗、高频交流受控电压源、交流输入采样模块、控制器，交流输入模块的一端与耦合阻抗的一端连接，耦合阻抗的另一端与高频交流受控电压源的正输出端连接,高频交流受控电压源的负输出端与交流输入模块的另一端连接，交流输入采样模块采样输入电流Iin和输入电压Vin得到输入电流Iin的幅值Iinm和相位
Figure PCTCN2016110552-appb-000001
及输入电压Vin的幅值Vinm和相位
Figure PCTCN2016110552-appb-000002
并送入控制器，控制器依据分数阶电容电流闭环控制算法对采样到的信号进行处理并产生控制信号D送至高频交流受控电压源，高频交流受控电压源根据控制信号D在正输出端和负输出端之间产生基波电压VF。
在上述所述的分数阶电容中，由基尔霍夫定律可知：
Figure PCTCN2016110552-appb-000003
由式可知在输入电压Vin已知的情况下，控制受控电压源输出基波电压VF可以使输入电流Iin为任意波形。因此，正确的控制输出基波电压VF，可以使输入电流Iin与输入电压Vin之间的关系在所需频率处满足分数阶电容的定义。
本发明所述的高频受控电压源是由可输出高频率的交流电压的高频交流 逆变电路构成，可向外输出有功功率，满足阶数大于1时分数阶电容的特性。高频交流逆变电路的基本工作原理是将控制信号D转化为脉冲宽度调制信号，以用来驱动电路中的开关管，从而控制电路的输出基波电压VF，以控制输入电流Iin在所需频率处与输入电压Vin之间的关系符合分数阶电容电流电压的关系。
进一步地，所述高频交流受控电压源由能输出高频率交流电压的高频交流逆变电路构成，高频交流受控电压源向外输出有功功率，实现阶数大于1，通过采用不同功率容量的受控电压源，实现不同功率等级的分数阶电容。
进一步地，所述的控制器由数字信号处理器构成。
进一步地，所述的分数阶电容电流闭环控制算法为基于相量分析的电流闭环控制算法，能避免在一个高频交流周期内逐点检测电压电流波形，减轻控制器的负担，且易于数字实现。
进一步地，所述分数阶电容电流闭环控制算法在数字信号处理器上运行实现，分数阶电容的容值和阶数通过在线修改软件参数可实现在线调节。
进一步地，所述的阶数α的取值范围如下：
α>1且α∈(4k+1,4k+2)
其中k为整数。
所述的分数阶电容电流闭环控制算法为基于“相量分析”控制方法，避免在一个高频交流周期内逐点检测电压电流波形，可以减轻控制器的负担，且易于数字实现。
所述阶数大于1的大功率可调高频分数阶电容的控制方法具体包括：
假设输入电压Vin，输入电流Iin和高频受控源输出电压VF在一个交流周期 内都是纯正弦的，且为同频正弦量。因为稳态情况下，高频交流分数阶电容工作时两端的电压是Vin正弦的，高频受控源输出电压VF也是正弦的，且可控制与Vin同频，所以这种假设是合理的。
当VF，Vin和Iin都为正弦时，它们的波形可仅由频率、幅值和初相位来描述，并可用“相量分析法”表示。以Vin的方向为实轴，超前其90度为虚轴，构造复平面，则可得VF、Vin和Iin相量形式及其在复平面上的表示为：
Figure PCTCN2016110552-appb-000004
Figure PCTCN2016110552-appb-000005
Figure PCTCN2016110552-appb-000006
其中
Figure PCTCN2016110552-appb-000007
和
Figure PCTCN2016110552-appb-000008
分别为受控电压源输出电压和输入电流超前输入电压的角度值。VFm分别为受控源输出电压的幅值。VF_REAL与VF_IMA分别为
Figure PCTCN2016110552-appb-000009
的实部和虚部，Iin_REAL与Iin_IMA分别为
Figure PCTCN2016110552-appb-000010
的实部和虚部。
控制器将电压采样器采样的输入电压转换成相量表示后，进行如下运算：
Figure PCTCN2016110552-appb-000011
式中
Figure PCTCN2016110552-appb-000012
是分数阶电容电流闭环控制算法电流给定信号Iref(t)的相量表示，Iref_REAL和Iref_IMA分别为其实部与虚部，Cα为分数阶电容的容值，α为分数阶电容的阶数，由上式可知电流给定信号Iref与输入电压Vin的关系为分数阶电容电流电压的关系。
电流给定信号
Figure PCTCN2016110552-appb-000013
与输入电流
Figure PCTCN2016110552-appb-000014
比较，得到的差值通过电流闭环控制算法，得到高频交流受控电压源的所需输出的电压
Figure PCTCN2016110552-appb-000015
并转化为控制信号D，以调节输入电流
Figure PCTCN2016110552-appb-000016
使输入电流
Figure PCTCN2016110552-appb-000017
跟踪电流给定信号
Figure PCTCN2016110552-appb-000018
即使得输入电流 与输入电压的关系为分数阶电容电流电压的关系。
与现有技术相比，本发明具有如下优点和技术效果：本发明提供的一种阶数大于1的大功率的可调高频分数阶电容，可工作在输入电压即分数阶电容电压为高频的时候，所得到的输入电流输入电压之间的关系在所需工作频率处与阶数大于1的分数阶电容的定义完全一致，还可以根据应用场合的需要，通过调整控制器的参数，灵活调节实现不同分数阶电容的阶数和容值，而且本发明所实现的分数阶电容功率由受控电压源决定，因此可选用不同功率等级的受控电压源以适应不同的功率应用场合。
附图说明
图1为实施方式中提供的阶数大于1的分数阶电容模型。
图2为实施方式中的D类谐振逆变器电路图。
图3为实施方式中的分数阶电容仿真原理图。
图4为实施方式中1.3阶分数阶电容的输入电压和输入电流的仿真波形图。
图5为实施方式中1.5阶分数阶电容的输入电压和输入电流的仿真波形图。
图6为实施方式中1.7阶分数阶电容的输入电压和输入电流的仿真波形图。
图7为实施方式中仿真模型的输入电流和输入电压波形。
具体实施方式
为进一步阐述本发明的内容和特点，以下结合附图对本发明的具体实施方案进行具体说明，但本发明的实施和保护不限于此。
本实例一种阶数大于1的大功率可调高频分数阶电容的基本原理是用控制器生成的控制信号对高频交流受控电压源的输出电压进行控制，使电路的输入电流和输入电压之间符合阶数大于1的分数阶电容的定义，整个电路相 当于一个分数阶电容。
如图1，一种阶数大于1的大功率可调分数阶电容，包括交流输入模块1、耦合阻抗2、高频交流受控电压源3、交流输入采样模块4、控制器5，交流输入模块1的一端A与耦合阻抗2的一端连接，耦合阻抗2的另一端与高频交流受控电压源3的正输出端P连接,高频交流受控电压源3的负输出端N与交流输入模块1的另一端B连接，交流输入采样模块4采样输入电流Iin和输入电压Vin得到输入电流Iin的幅值Iinm和相位
Figure PCTCN2016110552-appb-000019
及输入电压Vin的幅值Vinm和相位
Figure PCTCN2016110552-appb-000020
并送入控制器即数字信号处理器TMS320F28335，数字信号处理器依据分数阶电容电流闭环控制算法对采样到的信号进行处理并产生控制信号D送至高频交流受控电压源3，高频交流受控电压源3根据控制信号D在正输出端P和负输出端N之间产生基波电压VF。
如图1所示，高频受控电压源采用可输出高频率交流电压的高频交流逆变电路.在本例中，高频交流逆变电路采用D类谐振逆变器，如图2。其中Cr、Lr为串联谐振支路，R1为串联谐振支路的内阻，两个开关管互补导通，设上管S1的驱动波形占空比为D，与Vin的相位差为
Figure PCTCN2016110552-appb-000021
则可得S2两端的电压VDS的波形为与S1驱动波形同相位，幅值为直流侧电压值Vd的方波。对VDS进行傅里叶分解可得瞬时值表达式为：
Figure PCTCN2016110552-appb-000022
式中w为高频交流逆变电路的开关角频率即为分数阶电容的工作频率，式中n表示当前分量为第n次谐波。
则VDS经Lr、Cr串联谐振选频后，输出基波VF的瞬时值表达式为：
Figure PCTCN2016110552-appb-000023
在占空比D∈[0,0.5]的区间内基波VF的幅值与占空比是一一对应的关系，而且基波VF的相位
Figure PCTCN2016110552-appb-000024
与驱动波形的相位
Figure PCTCN2016110552-appb-000025
相同，因此控制S1的驱动波形的占空比和相位，就可以控制VF的幅值和相位。
数字信号处理器将采样到的电压电流信号转换成相量式表示，以输入电压Vin的方向为实轴，超前其90度为虚轴，构造复平面，则可得VF、Vin和Iin相量形式及其在复平面上的表示为：
Figure PCTCN2016110552-appb-000026
Figure PCTCN2016110552-appb-000027
式中
Figure PCTCN2016110552-appb-000028
为输入电流Iin与输入电压Vin的相位差，Iin_REAL和Iin_IMA分别输入电流向量
Figure PCTCN2016110552-appb-000029
的实部分量与虚部分量。
Figure PCTCN2016110552-appb-000030
Figure PCTCN2016110552-appb-000031
同时数字信号处理器对输入电压相量进行如下运算得到电流给定信号
Figure PCTCN2016110552-appb-000032
为：
Figure PCTCN2016110552-appb-000033
式中Cα和α分别为分数阶电容的容值和阶数，Iref_REAL和Iref_IMA分别电流给定信号
Figure PCTCN2016110552-appb-000034
的实部分量与虚部分量。
电流给定信号
Figure PCTCN2016110552-appb-000035
与输入电流
Figure PCTCN2016110552-appb-000036
比较，得到的差值通过电流闭环控制算法得到受控电压源需输出的电压向量
Figure PCTCN2016110552-appb-000037
本实施方式中采用的电流闭环控制 算法为带输入电压前馈补偿的比例控制，即
Figure PCTCN2016110552-appb-000038
式中GC为比例系数，VF_REAL和VF_IMA分别为向量
Figure PCTCN2016110552-appb-000039
的实部分量与虚部分量。
则
Figure PCTCN2016110552-appb-000040
的幅值VFm和相位
Figure PCTCN2016110552-appb-000041
分别为：
Figure PCTCN2016110552-appb-000042
Figure PCTCN2016110552-appb-000043
因此，通过实时采样Vin和Iin之间的相位差及各自幅值，并通过式(3)-(10)的运算，就可以得到
Figure PCTCN2016110552-appb-000044
的幅值和相位。从而避免了在一个交流周期内逐点采样电压电流波形。
又由式(2)可得
Figure PCTCN2016110552-appb-000045
对应所需驱动的占空比为：
Figure PCTCN2016110552-appb-000046
驱动相位则与
Figure PCTCN2016110552-appb-000047
的相位一致为：
Figure PCTCN2016110552-appb-000048
图3是一种阶数大于1的大功率分数阶电容在PSIM环境下的仿真原理图，其中电感L包括串联谐振支路的电感Lr和耦合电感Lf，分数阶电容电流闭环控制算法在数字信号处理器中执行，包括式(3)-(12)。在数字信号处理器中通过在线修改式(7)的Cα和α，可以实现在线调节分数阶电容的容值 和阶数。
设输入交流电压为100V/30kHz，直流电源电压为300V,电感L＝1085uH,电容C＝26.08nF,内阻r＝0.8Ω。
当模拟的分数阶电容为：Cα＝7×10-9，α＝1.3，f＝30kHz，仿真模型的输入电流和输入电压波形如图4所示，此时输入电流和输入电压相位差
Figure PCTCN2016110552-appb-000049
它们之间的关系与分数阶电容定义完全一致。
当模拟的分数阶电容为：Cα＝6×10-10，α＝1.5，f＝30kHz，仿真模型的输入电流和输入电压波形如图5所示，此时输入电流和输入电压相位差
Figure PCTCN2016110552-appb-000050
它们之间的关系与分数阶电容定义完全一致。
当模拟的分数阶电容为：Cα＝5.5×10-11，α＝1.7，f＝30kHz，仿真模型的输入电流和输入电压波形如图6所示，此时输入电流和输入电压相位差
Figure PCTCN2016110552-appb-000051
它们之间的关系与分数阶电容定义完全一致。
当模拟的分数阶电容由容值为7×10-9阶数为1.3在线调节到容值为5.5×10-11阶数为1.7时，仿真模型的输入电流和输入电压波形如图7，在t1时刻前，分数阶电容的容值和阶数分别为7×10-9和1.3，此时输入电流和输入电压相位差
Figure PCTCN2016110552-appb-000052
在t1时刻后，在线修改式(7)中的Cα和α，分别为Cα＝5.5×10-11，α＝1.7，经过400us后分数阶电容达到容值为5.5×10-11阶数为1.7,此时输入电流和输入电压相位差
Figure PCTCN2016110552-appb-000053
因此上述仿真验证了本发明的可行性和正确性。第一，可输出有功功率，满足阶数大于1时分数阶电容的特性；第二，可输出高频率的交流电压，满足分数阶电容高频工作的需求；第三，可根据应用场合设计控制信号，控制高频交流逆变电路器的输出电压，在线调整并实现不同容值和阶数的分数阶 电容；第四，分数阶电容的功率大小由高频交流逆变电路的额定功率决定，可以通过设计高频交流逆变电路的工作参数，实现不同功率等级的阶数大于1的分数阶电容，为今后阶数大于1的分数阶电容在各种功率场合的实际应用提供了参考。
上述实施例为本发明较佳的实施方式，但本发明的实施方式并不受所述实施例的限制，其他的任何未背离本发明的精神实质与原理下所作的改变、修饰、替代、组合、简化，均应为等效的置换方式，都包含在本发明的保护范围之内。

Claims (7)

  1. 一种阶数大于1的大功率可调高频分数阶电容，其特征在于包括交流输入模块(1)、耦合阻抗(2)、高频交流受控电压源(3)、交流输入采样模块(4)、控制器(5)，交流输入模块(1)的一端(A)与耦合阻抗(2)的一端连接，耦合阻抗(2)的另一端与高频交流受控电压源(3)的正输出端(P)连接,高频交流受控电压源(3)的负输出端(N)与交流输入模块(1)的另一端(B)连接，交流输入采样模块(4)采样输入电流Iin和输入电压Vin得到输入电流Iin的幅值Iinm和相位
    Figure PCTCN2016110552-appb-100001
    及输入电压Vin的幅值Vinm和相位
    Figure PCTCN2016110552-appb-100002
    并送入控制器，控制器依据分数阶电容电流闭环控制算法对采样到的信号进行处理并产生控制信号D送至高频交流受控电压源(3)，高频交流受控电压源(3)根据控制信号D在正输出端(P)和负输出端(N)之间产生基波电压VF。
  2. 根据权利要求1所述的一种阶数大于1的大功率可调高频分数阶电容，其特征在于所述高频交流受控电压源(3)由能输出高频率交流电压的高频交流逆变电路构成，高频交流受控电压源(3)向外输出有功功率，实现阶数大于1，通过采用不同功率容量的受控电压源，实现不同功率等级的分数阶电容。
  3. 根据权利要求1所述的一种阶数大于1的大功率可调高频分数阶电容，其特征在于所述的控制器(5)由数字信号处理器构成。
  4. 根据权利要求1所述的一种阶数大于1的大功率可调高频分数阶电容，其特征在于所述的分数阶电容电流闭环控制算法为基于相量分析的电流闭环控制算法。
  5. 根据权利要求1所述的一种阶数大于1的大功率可调高频分数阶电容， 其特征在于所述分数阶电容电流闭环控制算法在数字信号处理器上运行实现，分数阶电容的容值和阶数通过在线修改软件参数可实现在线调节。
  6. 根据权利要求1所述的一种阶数大于1的大功率可调高频分数阶电容，其特征在于所述的阶数为α，取值范围如下：
    α>1且α∈(4k+1,4k+2)
    其中k为整数。
  7. 用于权利要求1～6任一项所述的阶数大于1的大功率可调高频分数阶电容的控制方法，采用分数阶电容电流闭环控制算法为基于“相量分析法”，具体包括：假设输入电压Vin，输入电流Iin和高频受控源输出电压VF在一个交流周期内都是纯正弦的，且为同频正弦量；
    当VF，Vin和Iin都为正弦时，它们的波形能仅由频率、幅值和初相位来描述，并能用相量分析表示；以Vin的方向为实轴，超前其90度为虚轴，构造复平面，则得VF、Vin和Iin相量形式及其在复平面上的表示为：
    Figure PCTCN2016110552-appb-100003
    Figure PCTCN2016110552-appb-100004
    Figure PCTCN2016110552-appb-100005
    其中
    Figure PCTCN2016110552-appb-100006
    和
    Figure PCTCN2016110552-appb-100007
    分别为受控电压源输出电压和输入电流超前输入电压的角度值；VFm分别为受控源输出电压的幅值；VF_REAL与VF_IMA分别为
    Figure PCTCN2016110552-appb-100008
    的实部和虚部，Iin_REAL与Iin_IMA分别为
    Figure PCTCN2016110552-appb-100009
    的实部和虚部；
    控制器将交流输入采样模块采样的输入电压转换成相量表示后，进行如下运算：
    Figure PCTCN2016110552-appb-100010
    式中
    Figure PCTCN2016110552-appb-100011
    是分数阶电容电流闭环控制算法中电流给定信号Iref(t)的相量表示，Iref_REAL和Iref_IMA分别为其实部与虚部，Cα为分数阶电容的容值，α为分数阶电容的阶数，由上式可知电流给定信号Iref与输入电压Vin的关系为分数阶电容电流电压的关系；
    电流给定信号
    Figure PCTCN2016110552-appb-100012
    与输入电流
    Figure PCTCN2016110552-appb-100013
    比较，得到的差值通过电流闭环控制算法，得到高频交流受控电压源的所需输出的电压
    Figure PCTCN2016110552-appb-100014
    并转化为控制信号D，以调节输入电流
    Figure PCTCN2016110552-appb-100015
    使输入电流
    Figure PCTCN2016110552-appb-100016
    跟踪电流给定信号
    Figure PCTCN2016110552-appb-100017
    即使得输入电流与输入电压的关系为分数阶电容电流电压的关系。
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