CN110635690A - Fractional order KY converter and parameter design method thereof - Google Patents

Fractional order KY converter and parameter design method thereof Download PDF

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CN110635690A
CN110635690A CN201911029524.2A CN201911029524A CN110635690A CN 110635690 A CN110635690 A CN 110635690A CN 201911029524 A CN201911029524 A CN 201911029524A CN 110635690 A CN110635690 A CN 110635690A
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fractional order
voltage
fractional
converter
output
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王东东
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Chongqing Three Gorges University
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    • 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
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load

Abstract

The invention discloses a fractional order KY converter and a parameter design method thereof, comprising a direct-current voltage source (v)i) Fractional order output capacitance (C)α) Fractional order output inductor (L)β) Diode (D)b) Energy transfer capacitance (C)b) MOSFET tube (S)1And S2) Its body diode (D)1And D2) And a load R, MOSFET tube S1And MOSFET tube S2Form two working modes to supply direct current (v)i) The voltage is increased and provided for the load R, the fractional order KY converter realized by adopting the fractional order element is completely different from the existing DC/DC converter, the control dimension of parameter design is increased, the proper fractional order element order is selected through the parameter design, the frequency domain stability of the system is improved, the stability margin of the KY converter is improved, and the stability domain of the KY converter is enlarged.

Description

Fractional order KY converter and parameter design method thereof
Technical Field
The invention relates to the technical field of DC/DC converters, in particular to a fractional-order KY converter and a parameter design method thereof.
Background
The increasing global warming has led to an increasing demand for green energy, including solar cells, fuel cells, etc., and the electric energy generated from clean energy is generally not directly used due to its low voltage, so that a high-gain converter is required to convert the low voltage into a high voltage required by a load or a power grid, and the voltage ripple and noise at the output terminal become important criteria for the selection of the converter. For the traditional non-isolated voltage pump-up converter, the output current has large pulsation, so that the output voltage ripple becomes large, and the traditional non-isolated voltage pump-up converter cannot be directly used. In order to solve the problem, a capacitor and an inductor are generally required to be added in a circuit or a mode of increasing a switching frequency is required, in addition, a mode of adding a coupling inductor is also commonly adopted, and a KY converter is provided on the basis of comprehensively considering the modes, has no pulsation in output current and small output voltage ripple, and always works in a continuous conduction mode, so that the KY converter has great application potential.
Since the end of the last century, the application of fractional calculus theory in various subject fields, such as automatic control, nonlinear dynamics, mathematical modeling, nano materials and the like, is developed vigorously, and compared with the traditional integer order theory, the method can reflect or simulate physical phenomena in nature more accurately. The appearance of the fractional order element brings huge research heat for the application of the fractional order calculus theory in the field of electrical engineering, and because the fractional order modeling and analyzing method can simulate the phenomenon that the loss of the element changes along with the frequency, especially in a low-frequency or high-frequency region, the fractional order element does not need to be additionally added with a constant resistor in a circuit like an integer order, and the resistance value of the fractional order element cannot change along with the frequency.
In view of the great advantages of using fractional calculus theory to perform topology construction and parameter optimization design, it is necessary to provide a fractional-order KY converter.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a fractional-order KY converter and a parameter design method thereof.
The purpose of the invention is realized as follows:
a fractional order KY converter comprises a DC voltage source (v)i) Fractional order output capacitance (C)α) Fractional order output inductor (L)β) Diode (D)b) Energy transfer capacitance (C)b) MOSFET tube (S)1And S2) Its body diode (D)1And D2) And a load R, MOSFET tube (S)1And S2) Both ends are provided with a DC voltage source (v)i) And is connected with MOSFET (S)1And S2) In series, their body diodes (D)1And D2) Both ends of the MOSFET (S) are connected with the MOSFET1And S2) Across a DC voltage source (v)i) Is connected to a diode (D)b) Diode (D)b) And MOSFET tube S1The output end of the energy conversion capacitor (C) is connected with the energy conversion capacitor (C)b) Diode (D)b) And MOSFET tube S2The output end of the capacitor is connected with a fractional order output capacitor (C)α) And fractional order output inductance (L)β) Fractional order output capacitance (C)α) And fractional order output inductance (L)β) Series, fractional order output capacitance (C)α) Both ends of the power supply are connected with a load R and a MOSFET tube S1And MOSFET tube S2Form two working modes to supply direct current (v)i) The voltage rises and is supplied to the load R.
The voltage and current relationship of the fractional order output capacitor satisfies the equation:
Figure BDA0002249416360000021
and has a phase relationship: voltage hysteresis current
Figure BDA0002249416360000022
Here, iCFor fractional order of output capacitance current uCIs the fractional order of the output capacitor voltage, alpha is the order of the fractional order output capacitor, CαIs the capacitance of the fractional order output capacitor.
The voltage and current relationship of the fractional order output inductor satisfies the equation:
Figure BDA0002249416360000023
and has a phase relationship: current hysteresis voltage
Figure BDA0002249416360000024
Here, uLIs the voltage of a fractional-order output inductor, iLIs the current of the fractional order output inductor, beta is the order of the fractional order output inductor, LβIs the inductance of the fractional order output inductor.
A parameter design method of a fractional-order KY converter comprises the following steps: calculating MOSFET tube S1Open, MOSFET tube S2A mathematical model in a shutdown mode; calculating MOSFET tube S1Off, MOSFET tube S2Opening a mathematical model in a mode; then sequentially calculating a voltage transfer function Gvv(s) control output transfer function Gvd(s), transfer function
Figure BDA0002249416360000025
And transfer function Gid(s) frequency domain characteristics with respect to fractional order element order.
The invention has the beneficial effects that: the invention adopts the fractional order element to realize the fractional order KY converter, is completely different from the existing DC/DC converter, increases the control dimension of parameter design, selects the proper fractional order element order through the parameter design, improves the frequency domain stability of the system, improves the stability margin of the KY converter and increases the stability domain of the KY converter.
Drawings
FIG. 1 is a circuit diagram of the present invention;
fig. 2 is a power flow diagram of a fractional-order KY converter operating in mode 1;
fig. 3 is a power flow diagram of the fractional order KY converter operating in mode 2;
fig. 4 shows the voltage transfer function G when α ═ β ═ 1vv(s) bode diagram;
fig. 5 shows the voltage transfer function G when α ═ β ═ 0.7vv(s) bode diagram;
fig. 6 shows the control output transfer function G when α ═ β ═ 1vd(s) bode diagram;
fig. 7 shows the control output transfer function G when α ═ β ═ 0.7vd(s) bode diagram;
fig. 8 shows the transfer function G when α ═ β ═ 1ivi(s) bode diagram;
fig. 9 shows the transfer function G when α ═ β ═ 0.7ivi(s) bode diagram;
fig. 10 shows the transfer function G when α ═ β ═ 1id(s) bode diagram;
fig. 11 shows the transfer function G when α ═ β ═ 0.7idBode diagram of(s).
Detailed Description
The invention is further illustrated by the following figures and examples.
A fractional order KY converter comprises a DC voltage source (v)i) Fractional order output capacitance (C)α) Fractional order output inductor (L)β) Diode (D)b) Energy transfer capacitance (C)b) MOSFET tube (S)1And S2) Its body diode (D)1And D2) And a load R, MOSFET tube (S)1And S2) Both ends are provided with a DC voltage source (v)i) And is connected with MOSFET (S)1And S2) In series, their body diodes (D)1And D2) Both ends of the MOSFET (S) are connected with the MOSFET1And S2) Across a DC voltage source (v)i) Is connected to a diode (D)b) Diode (D)b) And MOSFET tube S1The output end of the energy conversion capacitor (C) is connected with the energy conversion capacitor (C)b) Diode (D)b) And MOSFET tube S2The output end of the capacitor is connected with a fractional order output capacitor (C)α) And fractional order output inductance (L)β) Fractional order output capacitance (C)α) And fractional order output inductance (L)β) Series, fractional order output capacitance (C)α) Both ends of the power supply are connected with a load R and a MOSFET tube S1And MOSFET tube S2Form two working modes to supply direct current (v)i) The voltage rises and is supplied to the load R.
The voltage and current relationship of the fractional order output capacitor satisfies the equation:
Figure BDA0002249416360000041
and has a phase relationship: voltage hysteresis currentHere, iCFor fractional order of output capacitance current uCIs the fractional order of the output capacitor voltage, alpha is the order of the fractional order output capacitor, CαIs the capacitance of the fractional order output capacitor. The voltage and current relationship of the fractional order output inductor satisfies the equation:
Figure BDA0002249416360000043
and has a phase relationship: current hysteresis voltage
Figure BDA0002249416360000044
Here, uLIs the voltage of a fractional-order output inductor, iLIs the current of the fractional order output inductor, beta is the order of the fractional order output inductor, LβIs the inductance of the fractional order output inductor.
A parameter design method of a fractional-order KY converter comprises the following steps: calculating MOSFET tube S1Open, MOSFET tube S2A mathematical model in a shutdown mode; calculating MOSFET tube S1Off, MOSFET tube S2Opening a mathematical model in a mode; then sequentially calculating a voltage transfer function Gvv(s) control output transfer function Gvd(s), transfer function
Figure BDA0002249416360000045
And transfer function Gid(s) the relationship between the frequency domain characteristics and the fractional order element order, the specific calculation process is as follows: as shown in FIG. 1, it is a circuit diagram of the fractional-order KY converter of the present invention, which passes through MOSFET (S)1And S2) And its body diode (D)1And D2) Diode (D)b) Energy transfer capacitance (C)b) A DC voltage source (v)i) And is connected to a fractional order output capacitor (C)α) And fractional order output inductance (L)β) And after filtering, connecting a direct current load R. Assume energy transfer capacitance (C)b) When the value is large enough, the voltage across the two terminals is viOutput voltage of voThe inductor current is i, as shown in fig. 1-3. As can be seen from fig. 1, the fractional order KY converter is a low-pass filter having two fractional order elements and always operates in a continuous conduction mode, and its mathematical model can be described by a fractional order differential equation.
1) Mode 1, as can be seen from FIG. 2, at this time S1Opening, S2And (3) turning off, wherein a differential equation of the turn-off is obtained according to the KVL law as follows:
Figure BDA0002249416360000051
2) mode 2, as can be seen from FIG. 3, at this time S2Opening, S1And (3) turning off, wherein a differential equation of the turn-off is obtained according to the KVL law as follows:
Figure BDA0002249416360000052
the state space average model of the fractional-order KY converter obtained by performing state averaging on the equations (1) and (2) is
Figure BDA0002249416360000053
Wherein the content of the first and second substances,<vi>、<vo>、<i>are each vi、voI average over a period, let Vi、VoI, D, each is vi、voThe direct current components of i, d,
Figure BDA0002249416360000054
are each vi、voI, d. Wherein the content of the first and second substances,
Figure BDA0002249416360000055
thus, can be aligned with<vi>、<vo>、<i > and d are decomposed as follows
Substituting equation (4) into equation (3) and ignoring higher order small quantities
Figure BDA0002249416360000062
Can obtain the product
Figure BDA0002249416360000063
Separating the direct current component in the formula (5), and defining the obtained static operating point equation based on the Caputo fractional order derivative as
Figure BDA0002249416360000064
The working point of the system in the steady state is obtained as
Figure BDA0002249416360000065
Separating the AC component of the formula (5) to obtain an AC small signal model of
Figure BDA0002249416360000066
The output voltage can be obtainedTo the input voltage
Figure BDA0002249416360000072
Transfer function G ofvv(s) is
Figure BDA0002249416360000073
Output voltage
Figure BDA0002249416360000074
For the duty ratio
Figure BDA0002249416360000075
I.e. the control output transfer function Gvd(s) is
Figure BDA0002249416360000076
Output currentTo the input voltage
Figure BDA0002249416360000078
Transfer function of
Figure BDA0002249416360000079
Is composed of
Figure BDA00022494163600000710
Output current
Figure BDA00022494163600000711
For the duty ratio
Figure BDA00022494163600000712
Transfer function G ofid(s) is
Figure BDA00022494163600000713
From the equations (9) and (10), the voltage transfer function Gvv(s) control output transfer function Gvd(s), transfer function
Figure BDA00022494163600000714
And transfer function GidThe frequency domain characteristic of(s) is not only related to inductance and capacitance values, but also related to the order of the fractional order element therein, and the change of the fractional order will have a great influence on the frequency domain characteristic thereof.
1) For voltage transfer function Gvv(s) the transformer parameters are taken as R ═ 1k Ω, L ═ 2.4uH, C ═ 1100uF, ViWhen D is 0.5 at 12V, the frequency domain characteristics are shown in fig. 4-5. As can be seen from fig. 4, under the selected parameter conditions, when α ═ β ═ 1, the phase angle margin has reached a critical state, which is detrimental to the stability of the system; when the fractional order element changes in order, i.e., α ═ β ═ 0.7, the phase angle margin is already satisfactory, as shown in fig. 5. The voltage transfer function can be stabilized due to the introduction of the fractional order.
2) Transfer function G for control outputvd(s) the transformer parameters are taken as R ═ 1k Ω, L ═ 2.4uH, C ═ 1100uF, ViWhen D is 0.5 at 12V, the frequency domain characteristics are shown in fig. 5-6. As can be seen from fig. 5, under the selected parameter conditions, when α ═ β ═ 1, the phase angle margin has reached the critical state; when the fractional order element changes in order, i.e., α ═ β ═ 0.7, the phase angle margin is already satisfactory, as shown in fig. 6. The control output transfer function can be stable due to the introduction of the fractional order.
3) For transfer function
Figure BDA0002249416360000081
The converter parameters are taken as R ═ 1k Ω, L ═ 2.4uH, C ═ 1100uF, ViWhen D is 0.5 at 12V, the frequency domain characteristics are shown in fig. 7-8. As can be seen from fig. 7, under the selected parameter conditions, when α ═ β ═ 1, the phase angle margin has reached the critical state; when the fractional order element changes in order, i.e., α ═ β ═ 0.7, the phase angle margin is already satisfactory, as shown in fig. 6.
4) For transfer function Gid(s) the transformer parameters are taken as R ═ 1k Ω, L ═ 2.4uH, C ═ 1100uF, ViWhen D is 0.5 at 12V, the frequency domain characteristics are shown in fig. 9-10. As can be seen from fig. 9, under the selected parameter conditions, when α ═ β ═ 1, the phase angle margin has reached the critical state; when the fractional order element changes in order, i.e., α ═ β ═ 0.7, the phase angle margin is already satisfactory, as shown in fig. 10.
In summary, the order of the fractional order element plays an important role in improving the stability of the KY converter, and can be stable even under the condition of parameters that cannot be stable in the integer order, so as to effectively increase the stability domain of the converter, and therefore, the order of the fractional order element can be selected according to the frequency domain characteristics to ensure the stable operation of the system
The invention adopts the fractional order element to realize the fractional order KY converter, is completely different from the existing DC/DC converter, increases the control dimension of parameter design, selects the proper fractional order element order through the parameter design, improves the frequency domain stability of the system, improves the stability margin of the KY converter and increases the stability domain of the KY converter.

Claims (4)

1. A fractional order KY converter characterized by: comprising a DC voltage source (v)i) Fractional order output capacitance (C)α) Fractional order output inductor (L)β) Diode (D)b) Energy transfer capacitance (C)b) MOSFET tube (S)1And S2) Its body diode (D)1And D2) And a load R, MOSFET tube (S)1And S2) Both ends are provided with a DC voltage source (v)i) And is connected with MOSFET (S)1And S2) In series, their body diodes (D)1And D2) Both ends of the MOSFET (S) are connected with the MOSFET1And S2) Across a DC voltage source (v)i) Is connected to a diode (D)b) Diode (D)b) And MOSFET tube S1The output end of the energy conversion capacitor (C) is connected with the energy conversion capacitor (C)b) Diode (D)b) And MOSFET tube S2The output end of the capacitor is connected with a fractional order output capacitor (C)α) And fractional order output inductance (L)β) Fractional order output capacitance (C)α) And fractional order output inductance (L)β) Series, fractional order output capacitance (C)α) Both ends of the power supply are connected with a load R and a MOSFET tube S1And MOSFET tube S2Form two working modes to supply direct current (v)i) The voltage rises and is supplied to the load R.
2. The fractional order KY converter of claim 1 wherein: the voltage and current relationship of the fractional order output capacitor satisfies the equation:
Figure FDA0002249416350000011
and has a phase relationship: voltage hysteresis current
Figure FDA0002249416350000012
Here, iCFor fractional order of output capacitance current uCIs a fractional order output capacitor voltage, alpha is a fractional order outputOrder of the capacitor, CαIs the capacitance of the fractional order output capacitor.
3. The fractional order KY converter of claim 1 wherein: the voltage and current relationship of the fractional order output inductor satisfies the equation:
Figure FDA0002249416350000013
and has a phase relationship: current hysteresis voltage
Figure FDA0002249416350000014
Here, uLIs the voltage of a fractional-order output inductor, iLIs the current of the fractional order output inductor, beta is the order of the fractional order output inductor, LβIs the inductance of the fractional order output inductor.
4. A method for designing parameters of a fractional-order KY converter as claimed in any of claims 1 to 3 wherein: the method comprises the following steps: calculating MOSFET tube S1Open, MOSFET tube S2A mathematical model in a shutdown mode; calculating MOSFET tube S1Off, MOSFET tube S2Opening a mathematical model in a mode; then sequentially calculating a voltage transfer function Gvv(s) control output transfer function Gvd(s), transfer function
Figure FDA0002249416350000015
And transfer function Gid(s) frequency domain characteristics with respect to fractional order element order.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112564480A (en) * 2020-11-24 2021-03-26 西安交通大学 Zero current detection circuit and KY converter with wide load range

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